Thomas Tuchel's side deservedly reached the final with goals from Timo Werner and Mason Mount.
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Chelsea reached their first UEFA Champions League final since 2012 with a comfortable 3-1 aggregate success against Real Madrid.
Match in brief
A high-tempo opening produced few chances and the tie did not take a decisive turn until midway though the first half. Then Edouard Mendy made a full-length save to thwart Karim Benzema and, shortly after, Chelsea took the lead when Timo Werner nodded in after Kai Havertz's clipped finish cannoned off the bar.
Havertz rattled the woodwork again soon after half-time and Mason Mount fired over as the hosts continued to create, but spurn, clear chances. Thibaut Courtois kept the Merengues alive with one-on-one saves from Havertz and N'Golo Kanté; however, his resistance was finally ended when substitute Christian Pulišić crossed for Mount to tap in late on.
Player of the Match: N'Golo Kanté (Chelsea)
"Covered a great deal of ground in a very close match. His transitions both from defence to attack and from attack to defence were excellent."
John Peacock, UEFA Technical Observer
Jon Phipps, Chelsea reporter
A deserved win for Chelsea but it should have been a lot more comfortable as their Achilles heel in front of goal was far too apparent once again. They were solid at the back, as is standard, yet could have avoided a nervy finale had they been able to put the finishing touch to any number of chances. But it's a night to celebrate, a third final appearance is booked and the positives of that have to outweigh any negatives.
Joe Walker, Real Madrid reporter
A night on which Madrid were thoroughly outclassed and, truth be told, that was the situation across both legs. They rode their luck and were still, somehow, in the game coming into the second half this evening but their formation and selection gamble really did not pay off. A deserved defeat for a tired-looking team who will come again, but perhaps need a refresh and a reboot this summer.
Mason Mount, Chelsea midfielder: "We should have probably had about five [goals]. To get that one late on, you could see what a massive goal it was for us. There's still one game left, and we go into every game to win. I haven't won anything yet and hopefully we can win. It's going to be a stunning game. It was a great performance tonight in a tough, tough game. We know what they're like – they were going to come and give it everything."
César Azpilicueta, Chelsea defender: "It was a massive performance – we could have scored more goals. Our aim was to keep a clean sheet against this team that has a lot of options. In the second half, clearly we were better. We had more chances and we had to suffer, but we fought really hard."
Casemiro, Real Madrid midfielder: "We were playing well in the opening 25 minutes. We had a couple of chances through Karim [Benzema] but then they started to play well and create chances. I think Chelsea were a better side than us and played better than we did. Today you saw [that] what we have achieved as a club is historic. It's not easy to win the Champions League as we have done."
• Chelsea have not lost a home match in which they scored the first goal in this competition since their 3-1 defeat by Atlético in the 2014 semi-finals.
• Thomas Tuchel (W2 D4) is the only manager to face Real Madrid six times in the competition without suffering a defeat.
• Mount became the first English goalscorer in the semi-finals since Wayne Rooney for Manchester United against Schalke just over ten years ago (26 April 2011).
• Chelsea became the sixth club to score 300 goals in the UEFA Champions League (group stage to final) after Real Madrid, Barcelona, Bayern, Manchester United and Juventus.
• Madrid have scored in 24 of their last 26 UEFA Champions League knockout phase matches. Both blanks came against English clubs – Liverpool and Chelsea.
• The visitors made it 12 UEFA Champions League games without a victory when trailing at half-time (D2 L10).
Chelsea: Mendy; Christensen, Thiago Silva, Rüdiger; Azpilicueta (James 88), Jorginho, Kanté, Chilwell; Havertz (Giroud 90), Werner (Pulišić 67), Mount (Ziyech 89)
Real Madrid: Courtois; Nacho, Éder Militão, Ramos, Mendy (Valverde 63); Kroos, Casemiro (Rodrygo 76), Modrić; Vinícius Júnior (Asensio 63), Benzema, Hazard (Mariano Díaz 89)
Chelsea still have five domestic matches to play before they take on Manchester City in the UEFA Champions League final in Istanbul on 29 May. Four of those are in the Premier League as they bid to seal a top-four finish, with the FA Cup final against Leicester (15 May) in the middle of those games.