Postpublished at 23:37 British Summer Time 4 July 2014
That's us done for the night then.
Enjoy the highlights and join us back here tomorrow for the final two quarter-finals.
Netherlands v Costa Rica
Argentina v Belgium
Brazil hold on to reach semi-finals
Hosts to play Germany in semi-final
Luiz the matchwinner with 40-yard free-kick
Rodriguez scores consolation penalty
Tom Rostance
That's us done for the night then.
Enjoy the highlights and join us back here tomorrow for the final two quarter-finals.
Netherlands v Costa Rica
Argentina v Belgium
The highlights show is about to start on BBC One and online. Tune in...
When in doubt, kick 'em out...
Former England defender Danny Mills
BBC Radio 5 live
"If you ask any professional footballer, they will do anything to get that medal round their neck. If you win the World Cup, in five or six years time nobody will care about how you got that there - you will be a legend.
"But this was just one game Brazil have played like this. Let's wait before saying they just kick lumps out of teams."
Colombia coach Jose Pekerman: "As regards everything that Colombia did during the World Cup, after being absent from the tournament for a long time we showed that we came here to play a wonderful World Cup, not just to participate.
"This is the most important thing that I can say about this national squad. Brazil needed the victory, every play there was a lot of intensity. That interrupted the game. We lost the fluidity of the game because of that intensity. There will always be decisive moves in matches such as this one, where a set piece can open up the result."
BBC Radio 5 live
South American football expert Tim Vickery: "Brazil will finally come up against a real European power in the match against Germany. They started against Croatia and had a bit of luck in that one. To take on Germany without Thiago Silva, and possibly without Neymar too, will be a tough ask but it is the game we want to see.
"The two sides have met only once before - in the 2002 World Cup final - and Germany will be out for revenge for that defeat."
If you missed any of the highlights from tonight's game they are at the top of the page, under the Highlights tab.
Enjoy that David Luiz goal. Again. And again...
BBC Radio 5 live
South American football expert Tim Vickery: "Over time the way to win has changed in Brazil. Leading up to the 1982 side, the way you won was by moving ball quicker than the opposition.
"Then they became obsessed with the physical side of things and got into a mind-set that said what Spain and Barcelona would go on to do with possession-based football was impossible.
"The success Spain and Barca enjoyed then threw them off-kilter, and there is a level of bitterness about that success.
"After Barcelona beat Santos, who then had Neymar, in the World Club Cup in 2011, Pep Guardiola really stuck the stiletto in. He said: 'We at Barcelona, we treat the ball in the same way my grandfather used to tell me Brazil did.'"
How much would it take to prize James Rodriguez away from Monaco do we reckon now?
Monaco spent £37m on his last summer. Double your money?
Early reports suggest that Neymar has been taken to hospital to have that back injury checked out.
Will bring you more on that as we get it...
BBC Sport Chief Football Writer Phil McNulty in Fortaleza
"Suitably ecstatic scenes here at Estadio Castelao but one of the main images will be the tearful young Colombian James Rodriguez, who has illuminated this World Cup. He showed he has the bravery to match his ability after some of the treatment meted out to him by Brazil. The saved all the consolation and comfort for Rodriguez until after the final whistle."
Former England defender Danny Mills
BBC Radio 5 live
"The South American way is win at all costs and you saw that today. Yes they gave away fouls, yes David Luiz was trying to put James Rodriguez off for the penalty, but if Brazil win this World Cup playing like that nobody will be bothered. If they lose, different story."
It looks like there is going to be some party on the Copacabana beach in Rio this evening.......
Chris Waddle
BBC Radio 5 live
"If Brazil win this World Cup they will be the worst team ever to win it.
"This Brazil side don't let anybody start passing the ball, they stop the game and obstruct the opposition when there is a problem. Julio Cesar has to get a red card there is no doubt, and Colombia will feel aggrieved to have lost. Brazil should have had five or six more yellow cards - they are getting away with murder.
"I feel for Colombia but they were overawed and realised too late that they had nothing to lose."
Gary Lineker
BBC Sport
"Colombian players walking off in tears being comforted by Brazilian players. Wonderfully sporting scenes after a great sporting contest."
Brazil now play Germany in Belo Horizonte on Tuesday night. A 21:00 BST kick-off. Get the sofa/pub reserved - you do not want to be missing that one!
Brazil will be without captain Thiago Silva - and maybe Neymar too...
Andy, via text: "What a stunning game of football, that is what the World Cup knockout stages are all about. I'm absolutely exhausted after that!"
Keith, via text: "Well done Brazil! Have to ask though - how on earth did Fernandinho get through that game without a booking?"
Owen Darlington:, external "Still not convinced by Brazil. Sad to see James go home. Colombia hard done by I think."
Jamie Millar: , external"The way Rodriguez was kicked all that game was a shambles. Thiago Silva out, Brazil look ordinary. Germany will 'av 'em."
Maria Pinilla:, external "Heartbroken. Literally sitting here crying. Well done Colombia, so so so so proud of you guys!"
BBC Radio 5 live
South American football expert Tim Vickery: "Colombia rallied towards the end but I wonder how much of that was Brazil collapsing and how much of it was their players running out of legs.
"Brazil worked like mad to stop Colombia having flow to win a scrappy game and I just wonder, although they keep winning , how many friends Brazil are losing around the world amongst those who have grown up with an image of what Brazilian football means."
Just two shots on target for Colombia in the end. Plenty to admire again from them but they've been done by a poor goal from a corner and then a goal for the ages...