Postpublished at 21:56 British Summer Time 13 April 2016
More from Antoine Griezmann, who scored both of Atletico's goals tonight: "We knew it would be different here. We've worked really hard defensively. We deserve it."
Atletico win 3-2 on aggregate
Benfica 2-2 Bayern Munich (2-3 agg)
Semi-final draw will be made on Friday
Emlyn Begley
More from Antoine Griezmann, who scored both of Atletico's goals tonight: "We knew it would be different here. We've worked really hard defensively. We deserve it."
Lionel Messi has not scored in 452 minutes for Barcelona, his longest spell without a club goal since April 2010. He'll exceed that goal drought if he doesn't score in the opening 23 minutes again against Valencia on Sunday.
Tonight was the first time he failed to get a shot on target in a Champions League since April 2014 - also against Atletico.
He's been stuck on 499 career goals since last month now.
Bayern Munich boss Pep Guardiola has made the Champions League semi-finals in each of his seven seasons as a manager.
Number seven sees him level with Carlo Ancelotti and Alex Ferguson in terms of semi-finals.
Atletico Madrid hero Antoine Griezmann: “The team has made a great effort to be among the best four of Europe.”
Griezmann has become only the second Atletico player to score more than five Champions League goals in a season after Diego Costa (who scored eight in 2013-14). The France forward has six, with two or three more games to go.
#bbceurofooty
BBunyanNgwiri: Glad to see barcelona out! So tired of the hype and praise and awe before them. Always moaning to the referee
Smark Twain: It's clear now, that whatever happens in the semi-finals, Man City are getting hammered by someone. Twice.
I'm not entirely sure about that - Real Madrid are beatable. And Bayern Munich have their flaws too. Not sure anybody would want to take on Atletico after that though.
A European focus
BBC Radio 5 Live
On BBC Radio 5 live from 22:00 BST the focus will be European football as Spanish football expert Andy Brassell and other guests discuss the Champions League semi-finalists.
#bbceurofooty
Robin Smit: I can't believe Barca are out of the Champions league, I had them down from the start to win it by a canter...
Callum Anderson: The 2015/16 Champions League just got very interesting.
The draw for the semi-finals is in Nyon on Friday at 10:30 BST (11:30 Swiss time).
And the team everybody wanted to avoid are out. Any of the four teams left in this tournament can win it. Without any doubt.
Atletico Madrid definitely deserved to go through over the two legs, Fernando Torres' red card in the first tie not proving costly in the end.
However they were lucky not to concede a penalty in the final minute for a Gabi handball. Had Barcelona scored, we would have had extra time. Mind you, there's every chance they'd have missed anyway on recent form.
Bayern Munich.
Atletico Madrid.
Real Madrid.
Manchester City.
Those are your Champions League semi-finalists.
This is only the second time in nine seasons Barcelona have failed to reach the Champions League semi-finals. They have both been quarter-final exits to Atletico Madrid.
It's hard to find words for just how good a job Diego Simeone has done at Atletico. A genius.
Atletico Madrid 2-0 Barcelona (3-2 agg)
The final whistle goes and Atletico Madrid claim a famous victory to knock champions Barcelona out of the Champions League.
Atletico Madrid 2-0 Barcelona (3-2 agg)
Sergi Roberto has the ball out wide for Barcelona but Filipe Luis gets it out and wins a goal kick in the process. How much longer can there be?! Six minutes of stoppage time gone.
Atletico Madrid 2-0 Barcelona (3-2 agg)
There can't be long left. Almost five minutes of stoppage time gone.
Atletico Madrid 2-0 Barcelona (3-2 agg)
I don't think we got an injury time announcement in all that drama. We're three and a half minutes into stoppage time.
Atletico Madrid 2-0 Barcelona (3-2 agg)
Atletico Madrid make a timewasting change three minutes into stoppage time. Stefan Savic comes on for Augusto Fernandez.
Atletico Madrid 2-0 Barcelona (3-2 agg)
Lionel Messi curls the ball over to a huge roar. We're into injury time now.