AS Roma pulled off one of the great Champions League comebacks by knocking Barcelona out with a remarkable 3-0 win in their quarter-final second leg, overcoming a 4-1 deficit from the first game to reach the last four on away goals.
In Tuesday's other match, Liverpool won the battle of Britain to knock out Premier League rivals Manchester City, 2-1 on the night and 5-1 over the two legs.
Roma's Kostas Manolas headed the decisive third goal in the 82nd minute, putting the Italians in the semi-finals for the first time since they reached the European Cup final in 1984 and making amends for his own goal in the first leg at the Nou Camp.
Roma forward Edin Dzeko had opened the scoring when he beat the offside trap and latched onto a perfectly weighted through ball from Daniele De Rossi to score in the sixth minute, lifting the hopes of the boisterous home fans in the Olympic Stadium.
Captain De Rossi converted a penalty in the 58th for the hosts after Dzeko was fouled by Gerard Pique, giving Roma a deserved second goal after Dzeko and his Czech strike partner Patrik Schick missed two clear chances each before the break.
"This would be a great triumph for any team, but for Roma and considering our story in European competitions, it’s truly incredible," De Rossi told reporters.
"We knew it would be difficult, but we had that little bit of belief. The first leg showed us Barcelona had a lot of quality, but not as much as a few years ago. We knew the gap between us and them wasn’t 4-1."
Barca fielded the team that thrashed Roma in the first leg with the help of two own goals and were overwhelming favourites to go through but the five-times European champions barely got a foothold in the game after falling behind to Dzeko's opener.
But Manchester City were unable to match Roma's achievement in overturning a three-goal deficit from the first leg.
They had trailed Liverpool 3-0 from last week's match but despite an early goal they couldn't capitalise.
That meant Liverpool reached the Champions League semi-finals for the first time in 10 years.
Mohamed Salah and Roberto Firmino struck decisive blows to secure a 2-1 win over Manchester City, 5-1 on aggregate.
City manager Pep Guardiola had said his team needed to produce a “perfect game” at the Etihad Stadium if they were to achieve a famous comeback and for 45 minutes they were not far off that level.
Yet it was Liverpool whose approach turned out to be perfect in the circumstances as they followed up some staunch first-half defending to level through Salah in the 56th minute and seal the tie through Firmino 13 minutes from fulltime, clinching their third win against City this season.
Gabriel Jesus had scored for the hosts after two minutes to fuel the home fans with hope and Guardiola's side had then launched wave after wave of attacks to pin Liverpool back.
Yet after Bernardo Silva hit the post in the 40th minute and Leroy Sane had an effort ruled out for a disputed offside two minutes later, City had just the solitary goal to show for their first-half exertions.
"It was quite difficult tonight, especially with the start," said Liverpool manager Juergen Klopp.
"This wonderful goal that we served them on a plate. I was expecting something like that but I liked the reaction immediately after that. They could’ve scored two or three goals in the first half but it was 100 percent clear that if we win the ball we’d have an opportunity."
After a glorious attacking display in the first leg, Liverpool did exactly what they had to do in Manchester and deservedly took their place in the semi-finals.
City can look back with some pride though on their first-half performance. They needed an early goal to set the mood and they got exactly that.
Liverpool defender Virgil van Dijk gave the ball away and Fernandinho played a superb pass to Raheem Sterling on the right who slipped the ball across to Jesus to slot home.