Real Madrid last won the Champions League in 2018Chelsea's reign as European champions came to an agonising end despite beating Real Madrid on a night of high drama at the Bernabeu Stadium.
In a Champions League epic, Mason Mount's wonderful finish and Antonio Rudiger's powerful header wiped out Real's 3-1 first-leg advantage and brought the quarter-final tie level in Spain's capital.
Thomas Tuchel's side were outstanding throughout and Timo Werner's clever finish from an angle put them ahead for the first time on aggregate and within sight of a place in the semi-finals.
But substitute Rodrygo - after a stunning pass by Luka Modric - forced extra time with a volleyed finish before Karim Benzema, a hat-trick hero in the first leg at Stamford Bridge six days earlier, headed the decisive goal in the 96th minute to send Real through 5-4 on aggregate.
Benzema, who had earlier headed against the bar on a rollercoaster night, was unmarked when he scored to break Chelsea's hearts after Rudiger slipped inside the box.
Even after what turned out to be the clincher, Hakim Ziyech, Kai Havertz and Jorginho went close to forcing a penalty shootout.
In the end Chelsea, who played superbly, were made to pay for their first-leg performance as Tuchel's side fell just short of producing one of the great comebacks in the competition.
Chelsea became just the second English team to score three goals away against Real Madrid in all European competition, after Manchester United did so in a 3-3 draw in the European Cup in May 1968Chelsea just fall short in classic
Many of Chelsea's players slumped to the ground at the end of 120 gripping minutes after pushing record 13-time winners Real - who will face Manchester City or Atletico Madrid in the last four - all the way.
Tuchel had said on the eve of this game that Chelsea's progression into the semi-finals would be akin to the best Hollywood script.
His players came close to producing a blockbuster in their first game at the Bernabeu in European competition as they showed incredible fight and belief - ingredients which were missing from their poor performance in the first leg.
This breathless game had everything and more, including a Marcos Alonso goal at 2-0 ruled out by the video assistant referee for handball.
While Tuchel will be delighted with the way his players responded, there will be concern at how much the energy-sapping 120 minutes has taken out of them.
Chelsea do not have long to recover from going out of Europe as they prepare to make a second visit of the season to Wembley.
They face Crystal Palace in an FA Cup semi-final on Sunday (16:30 BST) - a competition that offers them their last chance of landing a major domestic trophy.
Despite enjoying success in the Fifa Club World Cup and Uefa Super Cup, they lost a penalty shootout to Liverpool in the Carabao Cup final and are 12 points behind leaders Manchester City in the Premier League with just eight matches left.
Player of the match
MountMason Mount
Chelsea
Squad number19Player nameMount
Squad number2Player nameRüdiger
Squad number11Player nameWerner
Squad number24Player nameJames
Squad number29Player nameHavertz
Squad number3Player nameAlonso
Squad number6Player nameThiago Silva
Squad number8Player nameKovacic
Squad number7Player nameKanté
Squad number12Player nameLoftus-Cheek
Squad number16Player nameMendy
Squad number22Player nameZiyech
Squad number5Player nameJorginho
Squad number10Player namePulisic
Squad number17Player nameSaúl
Line-ups
Real Madrid
Formation 4-3-3
1Courtois
2Carvajal6Nacho4Alaba23Mendy
10Modric14Casemiro8Kroos
15Valverde9Benzema20Vinícius Júnior
1Courtois2CarvajalBooked at 118mins6NachoSubstituted forVázquezat 88'minutes4Alaba23MendySubstituted forMarceloat 78'minutes10Modric14CasemiroSubstituted forRodrygoat 78'minutes8KroosSubstituted forCamavingaat 73'minutesBooked at 90mins15ValverdeBooked at 68mins9BenzemaBooked at 37mins20Vinícius JúniorSubstituted forCeballosat 115'minutesSubstitutes
11Asensio12Marcelo13Lunin16Jovic17Vázquez18Bale19Ceballos21Rodrygo24Mariano25Camavinga40Fuidias41Marín ZamoraChelsea
Formation 3-4-1-2
16Mendy
24James6Thiago Silva2Rüdiger
12Loftus-Cheek7Kanté8Kovacic3Alonso
19Mount
29Havertz11Werner
16Mendy24JamesBooked at 10mins6Thiago Silva2Rüdiger12Loftus-CheekSubstituted forSaúlat 105'minutes7KantéSubstituted forZiyechat 100'minutesBooked at 102mins8KovacicSubstituted forJorginhoat 105'minutes3Alonso19Mount29HavertzBooked at 109mins11WernerSubstituted forPulisicat 83'minutesSubstitutes
1Arrizabalaga4Christensen5Jorginho10Pulisic13Bettinelli14Chalobah17Saúl22Ziyech28Azpilicueta31Sarr68ValeReferee:Szymon MarciniakAttendance:59,839Live Text
Match ends, Real Madrid 2, Chelsea 3.
Second Half Extra Time ends, Real Madrid 2, Chelsea 3.
Attempt blocked. Reece James (Chelsea) right footed shot from outside the box is blocked.
Foul by Christian Pulisic (Chelsea).
Dani Ceballos (Real Madrid) wins a free kick in the attacking half.
Attempt missed. Jorginho (Chelsea) left footed shot from the centre of the box misses to the right. Assisted by Hakim Ziyech following a corner.
Attempt missed. Hakim Ziyech (Chelsea) left footed shot from outside the box misses to the right following a corner.
Corner, Chelsea. Conceded by David Alaba.
Daniel Carvajal (Real Madrid) is shown the yellow card for a bad foul.
Hakim Ziyech (Chelsea) wins a free kick in the attacking half.
Foul by Daniel Carvajal (Real Madrid).
Attempt missed. Kai Havertz (Chelsea) header from the centre of the box is close, but misses the top right corner. Assisted by Reece James with a cross.
Attempt blocked. Jorginho (Chelsea) right footed shot from the centre of the box is blocked.
Corner, Chelsea. Conceded by Lucas Vázquez.
Substitution, Real Madrid. Dani Ceballos replaces Vinícius Júnior.
Attempt saved. Hakim Ziyech (Chelsea) left footed shot from the left side of the box is saved in the bottom left corner. Assisted by Mason Mount.
César Azpilicueta (Chelsea) is shown the yellow card.
Antonio Rüdiger (Chelsea) wins a free kick in the defensive half.
Foul by Rodrygo (Real Madrid).
Kai Havertz (Chelsea) is shown the yellow card for a bad foul.
