Phil McNulty
BBC Sport chief football writer at Anfield

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Jude Bellingham had the perfect stage to deliver a reminder of his quality after his recent much-discussed exclusion from head coach Thomas Tuchel's England squad.

Bellingham has been in form as Real lead La Liga, but he was largely anonymous as Liverpool controlled the game for virtually its entirety, apart from one breakthrough in the first half when he forced keeper Giorgi Mamardashvili to save with his feet.

In the end, like the rest of his team-mates, Bellingham was simply unable to make any serious impact in a disappointing display from the visitors.

Courtois showed why many place him alongside Liverpool keeper Alisson as the best in the world with a stunning display that threatened to earn his side a point they would not have deserved.

Vinicius was dominated by Bradley, while Mbappe was marginalised in an error-strewn performance.

It was an unhappy return to Anfield for Alexander-Arnold, who was given a fiercely hostile reception when he came on as substitute, while it was also a night of frustration for Real coach and former Liverpool midfielder Xabi Alonso, who could only watch on powerless as his team subsided.

Stephen Warnock
Former Liverpool defender on Football Daily

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Thibaut Courtois is an outstanding goalkeeper. There have been some other outstanding ones.

What you would say is, he has won all of the major competitions and he has done it exceptionally well at Real Madrid. He is definitely in line to be one of the best.

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Former Liverpool goalkeeper David James acknowledged the role Real Madrid Thibaut Courtois played in keeping the score at Anfield to only 1-0 in the Reds favour.

But he said Guillem Balague's assertion that the Belgian stopper was the "best goalkeeper in the world, probably the best ever" as a "stretch".

"A tremendous performance [from Liverpool] - I don't think 1-0 did it justice," James told 5 Live Breakfast.

"The performance from Courtois for Real Madrid was exceptional and it took an exceptional delivery by another exceptional player in Dominik Szoboszlai to set up Mac Allister for the goal.

"It was a very, very good performance. To say that he is the best in the world I think is still a stretch, but he definitely kept Liverpool at bay.

"A lot of the shots were ones you would expect him to save

"But I think it was the dominance of Liverpool's performance in the end that was the highlight."

Sam Drury
BBC Sport

Sorry, Guillem, but "probably the best goalkeeper ever"? I don't think I can go along with that.

Best goalkeeper in the world? Possibly. No doubt he's a fantastic keeper.

Definitely in the top two or three but, for what it's worth (somewhere between not much and absolutely nothing), I'm taking a fully fit Alisson Becker over Thibaut Courtois personally.

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Guillem Balague
Spanish football journalist on BBC Radio 5 Live

Thibaut Courtois is the best goalkeeper in the world. He probably is the best goalkeeper ever, but still doesn't get the recognition in England for some reason.

It gets on his nerves when that happens, so he gets motivated when he plays English sides, the same as he did in the Champions League final against Liverpool.

He was just outstanding - seven outstanding saves, five of them verging on miracle and the reason why it was only 1-0 at the end.

Thibaut Courtois got a brief mention in passing there and he was excellent last night.

And there has been a big claim made about the Real Madrid and Belgium goalkeeper in the aftermath...

Dale Johnson
Football issues correspondent

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• Referee Istvan Kovacs gave a free-kick to Liverpool against Aurelien Tchouameni for handball, an offence which appeared really close to being inside the area.
• It was checked by VAR.
• A factual decision, the position where the handball happened, would only be made by the VAR, not the referee.
• A referee is only sent to the monitor to judge a subjective decision, in this case handball. So by going to the screen, the referee was overturning his decision to give the handball.
• The handball factually took place inside the box which means it would be a penalty. And a penalty is reviewable by the VAR.
• If the handball had been confirmed as outside the area, the free-kick would have stood regardless of being right or wrong.
• Kovacs likely felt Tchouameni's arm was further out, but upon review, decided no horizontal barrier was being created.
• Because it's an overturned penalty, play restarts with the goalkeeper - effectively meaning Liverpool give up their attacking possession.

Sam Drury
BBC Sport

You're right on not becoming a bad team overnight, of course, James... but Liverpool gave it a good go.

In all seriousness, though, it seemed like more than a dip in form with issues around the structure of the team and integrating new players - all while a lot of established players were out of form.

Liverpool fans will be relieved that Arne Slot seems to have righted the ship in the past couple of games and they're showing just how good a side they are (always have been?).

While Conor Bradley was able to do a job on Vinicius Jr over on the right, Liverpool's central pairing of Virgil van Dijk and Ibrahima Konate dealt with Kylian Mbappe brilliantly.

Aside from a difficult half-volley on the edge of the box, Mbappe struggled to get involved in areas that could hurt the Reds.

He had 46 touches on the night and just five of those came in the Liverpool box.

The France forward's touch map highlights just how deep he had to drop in order to get involved in the game.

He had double the amount of touches (10) in his own half than he had in the Liverpool 18-yard box.

Not where you want your standout centre-forward to be...

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After starting the campaign with seven straight wins, Liverpool's season took a nasty turn with six defeats in their next seven - including four in a row in the Premier League.

But having stopped the rot with victory over Aston Villa at the weekend, Arne Slot's side kicked it up a notch on Tuesday by beating Real Madrid in a highly impressive performance at Anfield.

So have the Reds really turned the corner as they try to get their season back on track?

If so, the answer to their problems seems to have been pretty simple... go back to last season's winning formula.

Andy Robertson has come back in at left-back, the midfield trio of Ryan Gravenberch, Dominik Szoboszlai and Alexis Mac Allister has been reunited and suddenly things are clicking again.

It helps that players like Mac Allister and Mohamed Salah are starting to find form, too, of course.

Manchester City away on Sunday is the next big test but perhaps what will be most telling is how they fare when next faced with a team that does target them with long balls and set pieces aplenty.

For now, though, things are looking up for Liverpool. Do you think their recent woes are behind them? Use the thumbs below to let us know...

Time for the big question then...

David James
Former England goalkeeper on BBC Radio 5 Live

On the back of the win against Aston Villa at the weekend, I think things have just settled down a little bit.

Obviously it is easy to say when you have won two games and kept two clean sheets, but there just looked like this cohesion, which Arne Slot had been looking for [but not found] earlier on in the season.

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On a night full of positives for Liverpool, the performance of big-money summer signing Florian Wirtz was another.

Starting on the left, the Germany international impressed both with and without the ball.

Wirtz created five chances from open play for the second time in a Liverpool shirt (also vs Atletico Madrid) and is the only Premier League player to do so in more than one game across all competitions this season.

But for a brilliant save from Thibaut Courtois to deny Dominik Szoboszlai, he would have had another assist.

He also won possession six times, including three times in the final third.

Wirtz's long-term future may well be through the middle in a number 10 role, but might playing from the left be a way to get him into Arne Slot's XI while he gets up to speed?

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Virgil van Dijk called out Wayne Rooney's "over the top" criticism of him live on air after Liverpool's 1-0 win against Real Madrid on Tuesday.

The Liverpool captain spoke to match broadcasters Amazon Prime after the match, taking questions from pundits, including Rooney.

Last month on the Wayne Rooney Show, the former Manchester United striker criticised the body language of Van Dijk and Liverpool team-mate Mohamed Salah after a run of four consecutive Premier League defeats.

Van Dijk responded by accusing Rooney of "lazy criticism", before Rooney then doubled down on his comments.

On Tuesday they came face-to-face for the first time since the comments, resulting in slightly awkward encounter.

Here's how it unfolded:

Van Dijk: "If you lose four or five games in a row as a Liverpool player then it is a fair criticism, that is absolutely normal in that sense. But I think it is over the top at times as well at that point, but that is because we live in a world with so many platforms and so many people can say stuff, it will be picked up and made bigger. I think it is good that ex-players who played at the highest level who dealt with difficult moments as well puts a lot in perspective (said with a smile as Rooney laughs)."

Rooney: "I am not saying anything any more because I think I spurred them on and put them on a winning streak!

"I think what I've said was fair when you win the Premier League and then go on a run where you lose three or four games in a row, which you don't expect from Liverpool over the last few years.

"As Virgil is captain I think that is your opportunity to go and lead the players and that is what I was saying. That happens in football and I think the response has been great from Virgil and the team."

Van Dijk: "I think if you watched games then I would definitely take responsibility. I think the comment that I signed my new deal and then it was like 'that is it' and I let it slide, I think that was a bit... but that's my personal opinion and we move on."

It wasn't just the Liverpool fans with Trent Alexander-Arnold or even the players on the pitch, there was a little bit of needle in the post-match interviews as well...