Match ends, Real Madrid 1(5), Atlético de Madrid 1(3).
Real Madrid were crowned champions of Europe for the 11th time after beating Atletico Madrid in a dramatic penalty shootout in Milan.
Sergio Ramos' controversial finish put Zinedine Zidane's side ahead before Atletico striker Antoine Griezmann missed a penalty.
However, substitute Yannick Carrasco sent the Champions League final into extra-time with a close-range finish.
Cristiano Ronaldo struck the winning penalty after Juanfran had missed.
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How the penalty shootout unfolded
In the shootout, Lucas Vazquez, Marcelo and Gareth Bale scored for Real, with Griezmann, Gabi and Saul Niguez replying to make it 3-3.
After Ramos stepped up to make it 4-3, Juanfran hit the post, leaving Ronaldo with the chance to win the cup.
The competition's all-time leading scorer kept his composure to win it - his third individual Champions League triumph following on his from his successes with Manchester United in 2008 and Real in 2014.
Zidane's tactics deliver silverware
Zidane, a Champions League winner with Real as a player in 2002, replaced Rafael Benitez as manager at the Bernabeu in January, with Real still reeling from a bruising 4-0 hammering by Barcelona earlier in the season and facing the prospect of a second successive campaign without major silverware.
The 43-year-old finishes it as the seventh different manager to deliver a European Cup to Real.
As stylish as his side were going forward, they were just as impressive at the back as Atletico's attacking duo of Griezmann and Fernando Torres were starved of service before the interval.
Bale and Ronaldo repeatedly dropped back into midfield to help cut out the supply routes to Griezmann and Torres, while Karim Benzema also typified Real's work rate by doing his defensive duties.
Atletico were the better side after the break yet fortune was on Real's side as Pepe's rash challenge on Torres went unpunished and Stefan Savic stabbed another golden chance wide.
Bale shines ahead of Euro 2016
Bale was excellent as Real dominated the first half - powerful going forward and quick to help out at the back when required.
The Wales international was a danger at set pieces while he was heavily involved as his side took the lead.
Despite having an effort cleared off the line, Bale faded after the break and he spent most of extra-time limping around the pitch with cramp, unsurprising considering his work rate.
Yet he still put himself forward for the decisive shootout - and scored with a cool, low finish to help his team to a famous win.
What now for Simeone and Atletico?
Three weeks ago, Atletico were on course for a La Liga and Champions League double, yet Diego Simeone's side end the season without a trophy after the most heartbreaking of defeats.
Having finished three points behind champions Barcelona in Spain, they are left to reflect on what might have been despite an impressive second-half performance at the San Siro.
Griezmann became more dangerous but his missed penalty proved crucial, even though Carrasco later levelled after Juanfran's brilliant volleyed cross.
It is the third time Atletico have reached the final and failed to win yet the future remains bright, with Simeone likely to remain in charge next season despite earlier reported interest from Premier League clubs.
His task this summer will be keeping his assets, with Griezmann and midfielder Saul having been linked with moves to Chelsea and Manchester United respectively.
Clattenburg emerges with praise
England's Mark Clattenburg had his work cut out as he refereed a tempestuous derby, which saw eight bookings.
Real defender Pepe was at his theatrical best from the start as he tried to influence the Premier League official, who also had to calm down Simeone after Dani Carvajal's early foul on Griezmann.
Ramos put Real ahead from what looked like an offside position but Clattenburg's assistant kept his flag down.
However the 41-year-old from County Durham, who will be officiating at Euro 2016, was right to award the penalty which saw Griezmann hit the underside of the bar in the 47th minute.
Man of the match - Casemiro
What they said
Real Madrid boss Zinedine Zidane: "I've got a phenomenal squad who have fought and worked incredibly hard.
"We went into the game in good shape. Towards the end we suffered physically. The players had cramps but that's normal. Mentally, there's a lot of pressure. You have to fight and we've got there by working hard.
"Yes, I've dreamed about this. I'm positive. The president has given me the opportunity to coach this great club.
"I've got a phenomenal squad who have fought and worked incredibly hard. Having players with this kind of talent, you can achieve something great."
Atletico Madrid boss Diego Simeone: "You do your best, you try to do what you can, you get to two finals and you lose them both.
"One you lose 4-1, even though it was 2-1 for a long time, the other you lose on penalties.
"This cycle for me at Atletico, two finals in three years is, actually a marvellous achievement, but I am not happy with what I have achieved."
The stats you need to know
- Atletico have now contested more European Cup/Champions League finals without winning the trophy than any other club (three).
- This was the eighth Champions League final to go to extra-time, and the seventh to go to a penalty shootout.
- Zinedine Zidane is the second man (after Miguel Munoz) to win the European Cup/Champions League with Real Madrid as both a player and a manager.
- Zidane is the first French manager to win the Champions League.
- Sergio Ramos became the fifth player to score in two different Champions League finals, and the first defender to do so (also Raul, Samuel Eto'o, Lionel Messi and Cristiano Ronaldo).
- Indeed, Ramos joins Messi and Eto'o as one of three players to score in his first two Champions League finals.
- Antoine Griezmann became the first player since Arjen Robben in 2012 to miss a penalty in the Champions League final (excluding shootouts).
- Only Marcello Lippi (three) has lost more Champions League finals as a manager than Diego Simeone (two).
- 1NavasBooked at 47mins
- 15CarvajalBooked at 11minsSubstituted forDaniloat 52'minutesBooked at 93mins
- 3PepeBooked at 111mins
- 4RamosBooked at 90mins
- 14CasemiroBooked at 79mins
- 8KroosSubstituted forIscoat 72'minutes
- 9BenzemaSubstituted forVázquezat 77'minutes
- 7Cristiano Ronaldo
- 20Rodríguez Ruiz
- 20Torres Belén
- 3Filipe LuísSubstituted forHernándezat 109'minutes
- 14Fernández ArenasBooked at 90mins
- 12FernándezSubstituted forCarrascoat 45'minutes
- 6KokeSubstituted forParteyat 116'minutes
- 9TorresBooked at 61mins
- 5Cardoso Mendes
- Mark Clattenburg
- Shots on Target
Penalty Shootout ends, Real Madrid 1(5), Atlético de Madrid 1(3).
Goal! Real Madrid 1(5), Atlético de Madrid 1(3). Cristiano Ronaldo (Real Madrid) converts the penalty with a right footed shot to the bottom right corner.
Penalty missed! Still Real Madrid 1(4), Atlético de Madrid 1(3). Juanfran (Atlético de Madrid) hits the left post with a right footed shot.
Goal! Real Madrid 1(4), Atlético de Madrid 1(3). Sergio Ramos (Real Madrid) converts the penalty with a right footed shot to the bottom right corner.
Goal! Real Madrid 1(3), Atlético de Madrid 1(3). Saúl Ñíguez (Atlético de Madrid) converts the penalty with a left footed shot to the bottom left corner.
Goal! Real Madrid 1(3), Atlético de Madrid 1(2). Gareth Bale (Real Madrid) converts the penalty with a left footed shot to the bottom right corner.
Goal! Real Madrid 1(2), Atlético de Madrid 1(2). Gabi (Atlético de Madrid) converts the penalty with a right footed shot to the top left corner.
Goal! Real Madrid 1(2), Atlético de Madrid 1(1). Marcelo (Real Madrid) converts the penalty with a left footed shot to the bottom right corner.
Goal! Real Madrid 1(1), Atlético de Madrid 1(1). Antoine Griezmann (Atlético de Madrid) converts the penalty with a left footed shot to the bottom left corner.
Goal! Real Madrid 1(1), Atlético de Madrid 1. Lucas Vázquez (Real Madrid) converts the penalty with a right footed shot to the bottom right corner.
Penalty Shootout begins Real Madrid 1, Atlético de Madrid 1.
Second Half Extra Time ends, Real Madrid 1, Atlético de Madrid 1.
Corner, Real Madrid. Conceded by Lucas Hernández.
Attempt blocked. Danilo (Real Madrid) right footed shot from the right side of the box is blocked. Assisted by Lucas Vázquez.
Foul by Yannick Carrasco (Atlético de Madrid).
Pepe (Real Madrid) wins a free kick in the defensive half.
Attempt blocked. Lucas Vázquez (Real Madrid) right footed shot from the centre of the box is blocked. Assisted by Marcelo.
Attempt blocked. Cristiano Ronaldo (Real Madrid) left footed shot from outside the box is blocked. Assisted by Danilo.
Hand ball by Isco (Real Madrid).