Match ends, Real Madrid 3, VfL Wolfsburg 0.
Cristiano Ronaldo scored a superb hat-trick as Real Madrid overturned a 2-0 first-leg deficit against Wolfsburg to reach the Champions League semi-finals.
Wolfsburg arrived in Spain's capital protecting a healthy lead, but that was wiped out by a Ronaldo double in the space of 86 first-half seconds.
The Portuguese swept home the first from six yards before a glancing header levelled the scores on aggregate.
Ronaldo's hat-trick goal came from a free-kick when Wolfsburg's wall parted.
It completed a quite remarkable turnaround by the 10-time champions of Europe and keeps alive a season that looked to be over for Zinedine Zidane's side after last week's loss in Germany.
Ronaldo magic leaves Wolfsburg reeling
Three months ago Real fans were waving white handkerchiefs in a show of anger during the final throes of Rafael Benitez's short-lived reign.
On Tuesday, supporters gave the players a standing ovation after a dominant performance saw them advance to the semi-finals for the sixth successive season.
Ronaldo grabbed the match ball at the final whistle and placed it under his shirt as he lapped up the applause from the stands after his fifth Champions League treble - and third of this season.
The former Manchester United forward has 93 Champions League goals to his name in 125 appearances - 10 more than nearest rival Lionel Messi.
Yet, despite his hat-trick, this was a team effort from Zidane's side.
Sergio Ramos twice struck the woodwork while substitute Jese forced a fine one-handed from Diego Benaglio.
Can Real win it?
Real join Manchester City in Friday's draw (11:30 BST), with the winners of Atletico Madrid's tie with Barcelona and the game between Benfica and Bayern Munich to decide the remaining two places.
Real have come alive in recent weeks under Zidane, with a deserved El Clasico win over arch rivals Barcelona one of the highlights of their late season flourish.
Yet, as good as Real Madrid were, Wolfsburg were poor defensively after sitting back and inviting pressure.
Ronaldo was unmarked when he tapped home his first, while his third goal from a set-piece came after the German wall disintegrated.
While Barca will remain favourites to defend the trophy they won last June, Real are hitting form at the right time and cannot be ignored.
Man of the Match - Cristiano Ronaldo (Real Madrid)
What they said
Real Madrid boss Zinedine Zidane singled out Ronaldo for praise but added: "Cristiano needs the whole team, I want to speak about the team because they achieved this together.
"But he is special because not everyone is capable of scoring three goals."
Real Madrid forward Gareth Bale: "We have shown the world what we are capable of.
"We knew this was going to be a difficult test, but we felt we could really do it and we did."
Wolfsburg boss Dieter Hecking: "We should have defended better. To go to the next stage, we needed a goal.
"Two of the three goals were from dead balls and so that tells you that we didn't defend right."
The stats you need to know
- Ronaldo has now scored 34 goals (and has eight assists) in 36 Champions League knockout matches for Real Madrid.
- Ronaldo has scored in 62 different Champions League matches; more than any other player (Raul - 56, next most).
- The Portuguese forward has now scored 16 goals in the Champions League this season - only Ronaldo (17 in 2013-14) has more in a single CL campaign.
- This was only the third time in 16 occasions that a team losing 0-2 away in the first leg of a Champions League knockout tie have progressed after the second leg (after Barcelona v AC Milan in 2013 & Man Utd v Olympiakos in 2014).
- Real Madrid are still the only team yet to concede a goal at home in the Champions League this season.
Real, who trail by four points, now turn their attention to catching Barcelona at the top of La Liga and play struggling Getafe away on Saturday (15:00 BST).
Wolfsburg, eighth in the Bundesliga table, play on the same day away to Werder Bremen (14:30 BST).
- 19ModricSubstituted forVaraneat 90+2'minutes
- 9BenzemaSubstituted forRodríguez Ruizat 84'minutes
- 7Cristiano RonaldoBooked at 80mins
- 20Rodríguez Ruiz
- 8Vieira de FreitasBooked at 90mins
- 18Costa SantosBooked at 85mins
- 23GuilavoguiSubstituted forDostat 80'minutes
- 22DiasBooked at 76mins
- 16PintoSubstituted forCaligiuriat 72'minutes
- 27ArnoldBooked at 45mins
- 10DraxlerSubstituted forKruseat 32'minutes
- Viktor Kassai
- Shots on Target
Second Half ends, Real Madrid 3, VfL Wolfsburg 0.
Foul by Marcelo (Real Madrid).
Maximilian Arnold (VfL Wolfsburg) wins a free kick in the defensive half.
Substitution, Real Madrid. Raphael Varane replaces Luka Modric.
Vieirinha (VfL Wolfsburg) is shown the yellow card for a bad foul.
Gareth Bale (Real Madrid) wins a free kick in the attacking half.
Foul by Vieirinha (VfL Wolfsburg).
Attempt saved. Gareth Bale (Real Madrid) right footed shot from the centre of the box is saved in the bottom left corner.
Foul by Daniel Carvajal (Real Madrid).
Dante (VfL Wolfsburg) wins a free kick in the defensive half.
Corner, Real Madrid. Conceded by Diego Benaglio.
Attempt saved. Jesé (Real Madrid) right footed shot from the left side of the box is saved in the top right corner. Assisted by Gareth Bale.
Dante (VfL Wolfsburg) is shown the yellow card for a bad foul.
Cristiano Ronaldo (Real Madrid) wins a free kick in the defensive half.
Foul by Dante (VfL Wolfsburg).
Substitution, Real Madrid. Jesé replaces Karim Benzema.
Corner, Real Madrid. Conceded by Diego Benaglio.
Attempt saved. Karim Benzema (Real Madrid) right footed shot from the left side of the box is saved in the bottom right corner. Assisted by Pepe.
Cristiano Ronaldo (Real Madrid) is shown the yellow card for a bad foul.