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Real Madrid now stand between Bayern and a first final since they lifted the trophy in 2020 after Kimmich's second-half diving header earned a 3-2 aggregate win over Arsenal for Thomas Tuchel's men.

"Champions League games are always special, they're always special evenings, especially in the Allianz Arena, and you can see what we're capable of," said Manuel Neuer after the 1-0 win in which he recorded a 58th clean sheet in his 138th Champions League game, passing the previous record he shared with former Madrid goalkeeper Iker Casillas. 

Neuer watched from the opposite end as Bayern kept their English opponents at bay and then cut them open on occasion in a close contest. Both Leon Goretzka and Raphaël Guerreiro were denied by the woodwork early in the second half before the latter's perfectly timed cross was met by Kimmich's equally perfectly timed run.

"That was outstanding! The second half was very positive, we had dangerous attacks and could have scored even more goals," said Kimmich. "The bottom line is that we deserve to go through."

With the sides locked level at 2-2 after last week's first leg in London, it was perhaps no surprise that - bar a Gabriel Martinelli shot straight at Neuer - the opening 45 minutes were tense.

"The first half was a bit of a chess game from both sides," said Tuchel, who will be without the suspended Konrad Laimer for the first leg against Madrid after the Austria international picked up a second-half yellow card.

"We were very very strong in the second half. We showed more personality and courage, and deservedly won. I'm really proud of the team's performance."

Bayern can now look ahead to a 13th Champions League semi-final, only last-four opponents Madrid have tallied more. "That’s a good one to hear. The discipline we showed out there was crucial," said Neuer after a competition record 23rd quarter-final appearance for the Bayern captain.

Bayern will look to show the same quality and discipline in the first leg against Madrid at the Allianz Arena on 30 April or 1 May, with the second leg in the Spanish capital the following week.

If they win, and Dortmund see off Paris Saint-Germain in the other last-four tie, the German duo will reproduce the very same final of 2012/13, which was - like the 2023/24 final - also staged at the iconic Wembley Stadium.

"Dortmund and ourselves have to do our homework first," said Neuer, who was in the Bayern side that won the fifth of the club's six Champions League trophies with a 2-1 victory over Jürgen Klopp's men in London. "I wouldn't have anything against it."