Livakovic also saved three of four in Croatia’s last-16 shootout win over Japan. And he wasn't too shabby with his goalkeeping during the 120 minutes against Brazil, making a string of saves to keep the favourites at bay and take the game to a shootout.
At the other end of the field, though, will be a keeper who has also demonstrated an aptitude for brilliant shot-stopping and penalty heroics.
Emi Martinez is well known to fans in England so his efforts against the Netherlands won't have come as much of a surprise. He was excellent in the shootout, though, saving the first two Dutch spot-kicks, using psychological skills as well as technical ones.
It took informed observers back to the Copa America semi-final with Colombia last year when he was caught on microphones indulging in what is known in cricket as sledging. He would save three pens in that shootout to send Argentina to a final they won.
You almost want this to go to penalties just to see the contest between the two keepers.
None shall pass...
Argentina v Croatia (19:00 GMT)
If this game does go down to another penalty shootout tonight, Argentina will need to find a way past Croatia goalkeeper Dominik Livakovic, who has built himself a fine reputation for stopping spot-kicks.
Here are his heroics in the last round against Brazil...
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Thomas Holles: What a great game we have in prospect for tonight and a maybe another moment for Messi. Saying that though, I’m team Croatia tonight - I was disappointed to see how some of the Argentina players behaved after their QF victory and believe it right to see Croatia win.
Argentina on home turf?
Argentina v Croatia (19:00 GMT)
Chris Bevan
BBC Sport at Lusail Iconic Stadium
ReutersCopyright: Reuters
It's been said a few times already at this tournament that every time Argentina play it feels like a home game for them because of the sheer volume (in terms of numbers AND noise) of their fanatical support in Qatar, and it has certainly felt that way when I've been at their matches.
Tonight, though, they really are on familiar territory - they have played here at Lusail Stadium three times already, and their results reflect their journey at this World Cup: despair of defeat (to Saudi Arabia), relief of vital victory (against Mexico) and then the euphoria of a dramatic penalty shootout triumph (versus the Netherlands).
Croatia, in contrast, have not played here at all yet, although they will be hoping that they will get another go soon - whoever wins will be back here on Sunday for the final.
Outnumbered
Argentina v Croatia (19:00 GMT)
Shamoon Hafez
BBC Sport at Lusail Stadium
BBC SportCopyright: BBC Sport
Croatia fans are vastly outnumbered at the 80,000+ capacity Lusail Stadium, but there are more of them in than expected.
That bottom tier behind the goals is populated by red and white checked shirts.
The rest, however, is all blue and white and there was a huge roar when the Argentina players came out to warm-up.
Croatia are in their third World Cup semi-final, in their sixth tournament, and have again overachieved and Stimac was asked about the reasons behind their success.
“When you’re fighting for your lives, even when no-one is giving you a chance of becoming independent because we were not wanted at the beginning by any European countries or anyone," said Stimac.
"It was not similar to the Ukrainian situation now where everyone is very openly supporting Ukrainian people and giving them a chance to stay independent.
"It was not the same. Nobody was fighting for Croatia. Everybody was there, behind Yugoslavia to stay altogether.
“To survive in such circumstances defines who you are later on. That mental strength is deep inside our people and our nation. Survival. There is no difficulty we cannot overcome.
"Luka [Modric] was just a little boy when he lost his grandfather and when his family lost their home and they had to run away.
"This stays in you, in your culture and traditions. It will never be forgotten and that’s defining the character of our players."
'That's football'
Argentina v Croatia (19:00 GMT)
Argentina boss Lionel Scaloni has defended his players over accusations of misconduct and poor sportsmanship following their bad-tempered penalty shootout win over the Netherlands in the quarter-finals.
Argentina players mocked their Dutch opponents at the end of the match and Fifa subsequently opened disciplinary proceedings against both sides after the encounter saw a World Cup record of 18 yellow cards issued.
"The previous game was played the way we had to play - for both teams. That's football," Scaloni said.
"In some games things can happen like this. There can be arguments but that's all. That's why there's a referee.
"We need to put an end to this idea of thinking Argentina behave like this. We lost to Saudi Arabia and we didn't say anything.
"We won the Copa America in Brazil and experienced the most sporting behaviour with [Lionel] Messi, [Leandro] Paredes, Neymar, who were all sitting together in the tunnel in the Maracana [Stadium]. I'm really not convinced of this idea of unsporting behaviour."
Bit of niggle
Argentina v Croatia (19:00 GMT)
'Argentina ready for the midfield battle'
Argentina v Croatia (19:00 GMT)
Tim Vickery
BBC Sport South American football expert
Argentina have to prepare for 120 minutes, not just 90. Look at Croatia's recent record in tournament football, they know how to dictate the rhythm of the game, they know how to read the game.
Argentina have selected for a midfield battle, not to lose that battle in midfield. I think we're in for a really pleasant game, this could be one for the purists. One of nice midfield ebb and flow where both teams want to get onto the ball and dictate the rhythm.
We should get a really good spectacle which might unfold slowly over 90, perhaps 120 minutes.
Monday Night Club
There is still time to listen to the most recent Monday Night Club ahead of this game.
The team convened in Doha for a World Cup special. They discuss Gareth Southgate’s future with England and whether or not he would be a ‘sexy’ prospective manager for a Premier League club.
They ask if Antoine Griezmann should rank among the all-time greats of international football before looking ahead to the semi-finals with France against Morocco and Croatia against Argentina.
This is the third World Cup meeting between Argentina and Croatia, and first in the knockout stages. Argentina won the first 1-0 in 1998 thanks to a Mauricio Pineda goal.
Great World Cup, that.
Last time...
Argentina v Croatia (19:00 GMT)
It was only four years that these two last met in the World Cup, in the group stage.
A dreadful error from Willy Caballero set Croatia on their way to an impressive 3-0 win. The result left Argentina scrapping to qualify, which they did manage in second place in the group before France dealt with them in the last 16.
If things work out one way, Argentina could get revenge on both Croatia and France this winter.
Video content
Video caption: World Cup 2018: Argentina 0-3 CroatiaWorld Cup 2018: Argentina 0-3 Croatia
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SMS Message: Here we go again with Croatia being written off! What happened to that Brazil Argentina semi final everyone had pencilled in since the summer?! Argentina have huge talent on the pitch, but Croatia have the team. In knockout football it is more often the team that comes out on top. from Chris
Here we go again with Croatia being written off! What happened to that Brazil Argentina semi final everyone had pencilled in since the summer?! Argentina have huge talent on the pitch, but Croatia have the team. In knockout football it is more often the team that comes out on top.
Post update
Argentina v Croatia (19:00 GMT)
Andy Cryer
BBC Sport in Qatar
It's that song again...
The moment you get off the metro the Argentina hit that has gone viral is ringing in your ears.
Argentina football journalist Seba Onganelli on BBC Radio 5 Live: "It is going to be a really good game, but it will be a tough game for both sides. I am looking forward to it. Hopefully it will be a victory for Argentina, but it is going to be tough, maybe an extra-time victory.
"Croatia are a really good team, but I think Argentina know how to play these big games. I can't not mention Lionel Messi too, it is the best Messi I have seen. It is going to be tough tough, because both teams have really good players.
"I don't know if this is the last time we'll see Messi at a World Cup. He will be 39 at the next one, but I think it depends on this one."
'Emotion driving Argentina more than ever in Qatar'
Argentina v Croatia (19:00 GMT)
BBC SportCopyright: BBC Sport
Emotion is always a big part of how Argentina play, but it feels like it is driving us more than ever at this World Cup, with a place in the final only one step away.
Winning this tournament again after our triumphs in 1978 and 1986 always means so much to our players and our fans because of how important football is to our culture, but this time I think we are seeing a desperation for success that is different even to anything I experienced playing for the national team.
The excitement is always huge back home when we have the chance of winning any competition, but the reason I can feel it so much here too is because so many Argentina fans have come to Qatar.
The stadiums for all our games have been three-quarters full of our supporters, creating an incredible atmosphere and giving our players huge backing.
It's been like a big adventure for them, and it's brilliant to see - and hear. They don't just sing and dance for 90 minutes, they start an hour before the game and stay for as long afterwards, and just keep on making noise.
They are here for two reasons: partly because our 36-game unbeaten run before the tournament started had raised expectations, but mainly because it is probably Lionel Messi's final opportunity to win the World Cup.
How will the irresistible force of Lionel Messi fare when he comes up against the immovable object of Croatia here at Lusail Stadium?
Croatia have a genius of their own in Luka Modric and both have been on the losing side in World Cup Finals in the past so this has a sense of unfinished business.
Argentina's fans are here is vast numbers but Croatia will have their usual passionate support. The latter will be backing a team full of passion, character and - just in case anyone forgets - talent.
Sutton's prediction
Argentina v Croatia (19:00 GMT)
BBC SportCopyright: BBC Sport
I put my hands up here because I have written off Croatia numerous times throughout this tournament - and I don't mind saying I've got them badly wrong.
They are brilliantly organised and, at 37, Luka Modric is still so influential. They can keep the ball to control games and are extremely resilient.
True, they lack a cutting edge at times but they found a goal when it mattered against Brazil in their quarter-final and also appear happy to go the distance.
If this tie goes to penalties too, then no-one will fancy facing goalkeeper Dominik Livakovic from the spot after his heroics in the past two rounds.
So, this is going to be an extremely difficult game for Argentina, but I think it will help that they won't under-estimate Croatia on Tuesday, and will know what to expect.
Argentina are without both full-backs, Gonzalo Montiel and Marcos Acuna, through suspension after their yellow cards in what turned out to be a pretty crazy game with the Netherlands last time out.
When Lionel Messi put Argentina 2-0 up, it looked like they were through, but the Dutch responded with some brutally direct football to level and probably would have won it if they had continued playing that way in extra-time.
Who knows how this game will play out and I would say it is 50-50 in terms of who will win. But I haven't done too badly following my heart rather than my head at this tournament, so I am going to do it again and send Messi through to the final.
I always say Diego Maradona is the best footballer ever and he won the World Cup in 1986. Messi's amazing career could be labelled incomplete by some people unless he does the same but now he is two games away from achieving it - and I'd love to see it happen.
His pass for Argentina's first goal against the Dutch was phenomenal and shows he can still dictate little moments in games, even if he cannot do it for the entire 90 minutes like he used to.
They will need more of the same from him here and they also need to keep their heads, because they seem to play on the edge most of the time. Do that and they will get through.
Yes, this means I am writing off Croatia yet again - which probably means another shootout, which they will win.
Sutton's prediction: 1-0
'Croatia's midfield trio have a great bond'
Argentina v Croatia (19:00 GMT)
BBC World Service
Croatia Nova TV broadcaster Sasa Lugonjic on BBC World Service's World Football in Qatar podcast, talking about their midfield trio of Luka Modric, Mateo Kovacic and Marcelo Brozvoic: "They are amazing players. We don't have to talk about Luka Modric, he is one of the best midfielders in the history of football. You will know Kovacic well from the Premier League, and he is an amazing footballer, and then there is Marcelo Brozovic, who plays for Inter Milan, too.
"It is really special because in 1998 we had a special trio and for many years people in Croatia were saying they were 'an amazing trio and we will never a trio like that again' and then came Russia in 2018 and now we've got this. They suit each other well and they have a great bond and connection privately as well."
'Croatia potentially have the best technically-gifted midfield in the world'
Argentina v Croatia (19:00 GMT)
Croatia football journalist Ivan Renic on BBC Radio 5 Live: "If we got to extra time we know what will happen! I hope Croatia will do it in 90 minutes this time. They are full of confidence. They are shining. They are stable and they have a great head coach, he's made them strong and made them believe they can beat everyone. Nothing is impossible for them.
"Argentina have Lionel Messi, who is the greatest player of all-time, but if you look technically at the players we have, probably, the best midfield in the world. Technically they are potentially the best.
"Luke Modric is brilliant. His impact and influence on the game is amazing. He is attacking, he is defending, passing and shooting - he is doing everything for Croatia and he has been for over 15 years. This is his last World Cup, he's already done his magic, and this is just another great story and hopefully we can go to the end.
Live Reporting
Phil Dawkes
All times stated are UK
Excellent Emi
Argentina v Croatia (19:00 GMT)
Livakovic also saved three of four in Croatia’s last-16 shootout win over Japan. And he wasn't too shabby with his goalkeeping during the 120 minutes against Brazil, making a string of saves to keep the favourites at bay and take the game to a shootout.
At the other end of the field, though, will be a keeper who has also demonstrated an aptitude for brilliant shot-stopping and penalty heroics.
Emi Martinez is well known to fans in England so his efforts against the Netherlands won't have come as much of a surprise. He was excellent in the shootout, though, saving the first two Dutch spot-kicks, using psychological skills as well as technical ones.
It took informed observers back to the Copa America semi-final with Colombia last year when he was caught on microphones indulging in what is known in cricket as sledging. He would save three pens in that shootout to send Argentina to a final they won.
You almost want this to go to penalties just to see the contest between the two keepers.
None shall pass...
Argentina v Croatia (19:00 GMT)
If this game does go down to another penalty shootout tonight, Argentina will need to find a way past Croatia goalkeeper Dominik Livakovic, who has built himself a fine reputation for stopping spot-kicks.
Here are his heroics in the last round against Brazil...
Get Involved
#bbcfootball or text 81111 (UK only - standard message rates apply)
Thomas Holles: What a great game we have in prospect for tonight and a maybe another moment for Messi. Saying that though, I’m team Croatia tonight - I was disappointed to see how some of the Argentina players behaved after their QF victory and believe it right to see Croatia win.
Argentina on home turf?
Argentina v Croatia (19:00 GMT)
Chris Bevan
BBC Sport at Lusail Iconic Stadium
It's been said a few times already at this tournament that every time Argentina play it feels like a home game for them because of the sheer volume (in terms of numbers AND noise) of their fanatical support in Qatar, and it has certainly felt that way when I've been at their matches.
Tonight, though, they really are on familiar territory - they have played here at Lusail Stadium three times already, and their results reflect their journey at this World Cup: despair of defeat (to Saudi Arabia), relief of vital victory (against Mexico) and then the euphoria of a dramatic penalty shootout triumph (versus the Netherlands).
Croatia, in contrast, have not played here at all yet, although they will be hoping that they will get another go soon - whoever wins will be back here on Sunday for the final.
Outnumbered
Argentina v Croatia (19:00 GMT)
Shamoon Hafez
BBC Sport at Lusail Stadium
Croatia fans are vastly outnumbered at the 80,000+ capacity Lusail Stadium, but there are more of them in than expected.
That bottom tier behind the goals is populated by red and white checked shirts.
The rest, however, is all blue and white and there was a huge roar when the Argentina players came out to warm-up.
'There is no difficulty we cannot overcome'
Argentina v Croatia (19:00 GMT)
BBC World Service
Former Croatia coach Igor Stimac joined BBC World Service's World Football in Qatar podcast to preview the semi-final and reflect on their tournament so far.
Croatia are in their third World Cup semi-final, in their sixth tournament, and have again overachieved and Stimac was asked about the reasons behind their success.
“When you’re fighting for your lives, even when no-one is giving you a chance of becoming independent because we were not wanted at the beginning by any European countries or anyone," said Stimac.
"It was not similar to the Ukrainian situation now where everyone is very openly supporting Ukrainian people and giving them a chance to stay independent.
"It was not the same. Nobody was fighting for Croatia. Everybody was there, behind Yugoslavia to stay altogether.
“To survive in such circumstances defines who you are later on. That mental strength is deep inside our people and our nation. Survival. There is no difficulty we cannot overcome.
"Luka [Modric] was just a little boy when he lost his grandfather and when his family lost their home and they had to run away.
"This stays in you, in your culture and traditions. It will never be forgotten and that’s defining the character of our players."
'That's football'
Argentina v Croatia (19:00 GMT)
Argentina boss Lionel Scaloni has defended his players over accusations of misconduct and poor sportsmanship following their bad-tempered penalty shootout win over the Netherlands in the quarter-finals.
Argentina players mocked their Dutch opponents at the end of the match and Fifa subsequently opened disciplinary proceedings against both sides after the encounter saw a World Cup record of 18 yellow cards issued.
"The previous game was played the way we had to play - for both teams. That's football," Scaloni said.
"In some games things can happen like this. There can be arguments but that's all. That's why there's a referee.
"We need to put an end to this idea of thinking Argentina behave like this. We lost to Saudi Arabia and we didn't say anything.
"We won the Copa America in Brazil and experienced the most sporting behaviour with [Lionel] Messi, [Leandro] Paredes, Neymar, who were all sitting together in the tunnel in the Maracana [Stadium]. I'm really not convinced of this idea of unsporting behaviour."
Bit of niggle
Argentina v Croatia (19:00 GMT)
'Argentina ready for the midfield battle'
Argentina v Croatia (19:00 GMT)
Tim Vickery
BBC Sport South American football expert
Argentina have to prepare for 120 minutes, not just 90. Look at Croatia's recent record in tournament football, they know how to dictate the rhythm of the game, they know how to read the game.
Argentina have selected for a midfield battle, not to lose that battle in midfield. I think we're in for a really pleasant game, this could be one for the purists. One of nice midfield ebb and flow where both teams want to get onto the ball and dictate the rhythm.
We should get a really good spectacle which might unfold slowly over 90, perhaps 120 minutes.
Monday Night Club
There is still time to listen to the most recent Monday Night Club ahead of this game.
The team convened in Doha for a World Cup special. They discuss Gareth Southgate’s future with England and whether or not he would be a ‘sexy’ prospective manager for a Premier League club.
They ask if Antoine Griezmann should rank among the all-time greats of international football before looking ahead to the semi-finals with France against Morocco and Croatia against Argentina.
Listen here on BBC Sounds.
The only other meeting
Argentina v Croatia (19:00 GMT)
This is the third World Cup meeting between Argentina and Croatia, and first in the knockout stages. Argentina won the first 1-0 in 1998 thanks to a Mauricio Pineda goal.
Great World Cup, that.
Last time...
Argentina v Croatia (19:00 GMT)
It was only four years that these two last met in the World Cup, in the group stage.
A dreadful error from Willy Caballero set Croatia on their way to an impressive 3-0 win. The result left Argentina scrapping to qualify, which they did manage in second place in the group before France dealt with them in the last 16.
If things work out one way, Argentina could get revenge on both Croatia and France this winter.
Video content
Get Involved
Text 81111 (UK only - standard message rates apply)
Post update
Argentina v Croatia (19:00 GMT)
Andy Cryer
BBC Sport in Qatar
It's that song again...
The moment you get off the metro the Argentina hit that has gone viral is ringing in your ears.
You can read more about Messi's favourite song here.
'Argentina know how to play these big games'
Argentina v Croatia (19:00 GMT)
Argentina football journalist Seba Onganelli on BBC Radio 5 Live: "It is going to be a really good game, but it will be a tough game for both sides. I am looking forward to it. Hopefully it will be a victory for Argentina, but it is going to be tough, maybe an extra-time victory.
"Croatia are a really good team, but I think Argentina know how to play these big games. I can't not mention Lionel Messi too, it is the best Messi I have seen. It is going to be tough tough, because both teams have really good players.
"I don't know if this is the last time we'll see Messi at a World Cup. He will be 39 at the next one, but I think it depends on this one."
'Emotion driving Argentina more than ever in Qatar'
Argentina v Croatia (19:00 GMT)
Emotion is always a big part of how Argentina play, but it feels like it is driving us more than ever at this World Cup, with a place in the final only one step away.
Winning this tournament again after our triumphs in 1978 and 1986 always means so much to our players and our fans because of how important football is to our culture, but this time I think we are seeing a desperation for success that is different even to anything I experienced playing for the national team.
The excitement is always huge back home when we have the chance of winning any competition, but the reason I can feel it so much here too is because so many Argentina fans have come to Qatar.
The stadiums for all our games have been three-quarters full of our supporters, creating an incredible atmosphere and giving our players huge backing.
It's been like a big adventure for them, and it's brilliant to see - and hear. They don't just sing and dance for 90 minutes, they start an hour before the game and stay for as long afterwards, and just keep on making noise.
They are here for two reasons: partly because our 36-game unbeaten run before the tournament started had raised expectations, but mainly because it is probably Lionel Messi's final opportunity to win the World Cup.
Read more here.
Can Croatia tough it out again?
Argentina v Croatia (19:00 GMT)
Phil McNulty
BBC Sport chief football writer at Lusail Stadium
How will the irresistible force of Lionel Messi fare when he comes up against the immovable object of Croatia here at Lusail Stadium?
Croatia have a genius of their own in Luka Modric and both have been on the losing side in World Cup Finals in the past so this has a sense of unfinished business.
Argentina's fans are here is vast numbers but Croatia will have their usual passionate support. The latter will be backing a team full of passion, character and - just in case anyone forgets - talent.
Sutton's prediction
Argentina v Croatia (19:00 GMT)
I put my hands up here because I have written off Croatia numerous times throughout this tournament - and I don't mind saying I've got them badly wrong.
They are brilliantly organised and, at 37, Luka Modric is still so influential. They can keep the ball to control games and are extremely resilient.
True, they lack a cutting edge at times but they found a goal when it mattered against Brazil in their quarter-final and also appear happy to go the distance.
If this tie goes to penalties too, then no-one will fancy facing goalkeeper Dominik Livakovic from the spot after his heroics in the past two rounds.
So, this is going to be an extremely difficult game for Argentina, but I think it will help that they won't under-estimate Croatia on Tuesday, and will know what to expect.
Argentina are without both full-backs, Gonzalo Montiel and Marcos Acuna, through suspension after their yellow cards in what turned out to be a pretty crazy game with the Netherlands last time out.
When Lionel Messi put Argentina 2-0 up, it looked like they were through, but the Dutch responded with some brutally direct football to level and probably would have won it if they had continued playing that way in extra-time.
Who knows how this game will play out and I would say it is 50-50 in terms of who will win. But I haven't done too badly following my heart rather than my head at this tournament, so I am going to do it again and send Messi through to the final.
I always say Diego Maradona is the best footballer ever and he won the World Cup in 1986. Messi's amazing career could be labelled incomplete by some people unless he does the same but now he is two games away from achieving it - and I'd love to see it happen.
His pass for Argentina's first goal against the Dutch was phenomenal and shows he can still dictate little moments in games, even if he cannot do it for the entire 90 minutes like he used to.
They will need more of the same from him here and they also need to keep their heads, because they seem to play on the edge most of the time. Do that and they will get through.
Yes, this means I am writing off Croatia yet again - which probably means another shootout, which they will win.
Sutton's prediction: 1-0
'Croatia's midfield trio have a great bond'
Argentina v Croatia (19:00 GMT)
BBC World Service
Croatia Nova TV broadcaster Sasa Lugonjic on BBC World Service's World Football in Qatar podcast, talking about their midfield trio of Luka Modric, Mateo Kovacic and Marcelo Brozvoic: "They are amazing players. We don't have to talk about Luka Modric, he is one of the best midfielders in the history of football. You will know Kovacic well from the Premier League, and he is an amazing footballer, and then there is Marcelo Brozovic, who plays for Inter Milan, too.
"It is really special because in 1998 we had a special trio and for many years people in Croatia were saying they were 'an amazing trio and we will never a trio like that again' and then came Russia in 2018 and now we've got this. They suit each other well and they have a great bond and connection privately as well."
'Croatia potentially have the best technically-gifted midfield in the world'
Argentina v Croatia (19:00 GMT)
Croatia football journalist Ivan Renic on BBC Radio 5 Live: "If we got to extra time we know what will happen! I hope Croatia will do it in 90 minutes this time. They are full of confidence. They are shining. They are stable and they have a great head coach, he's made them strong and made them believe they can beat everyone. Nothing is impossible for them.
"Argentina have Lionel Messi, who is the greatest player of all-time, but if you look technically at the players we have, probably, the best midfield in the world. Technically they are potentially the best.
"Luke Modric is brilliant. His impact and influence on the game is amazing. He is attacking, he is defending, passing and shooting - he is doing everything for Croatia and he has been for over 15 years. This is his last World Cup, he's already done his magic, and this is just another great story and hopefully we can go to the end.