Match ends, Roma 3, Barcelona 0.
Roma pulled off a sensational second-leg comeback to beat Barcelona 3-0 and reach the Champions League semi-finals on away goals.
Barca were heavy favourites to progress after a 4-1 first-leg win, but fell apart to Roma's brilliant showing.
Defender Kostas Manolas scored the crucial third goal, heading in at the near post with eight minutes remaining.
Edin Dzeko struck early to give Roma hope and Daniele de Rossi added a second-half penalty.
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The crowd at the Stadio Olimpico erupted at the final whistle as the Roma substitutes and coaching staff piled on to the pitch to celebrate with the players.
There were tears in the stands from those watching, not quite believing what they had witnessed.
Roma deserve superb win
Roma became only the third team in Champions League history to overturn a first-leg defeat of three goals or more - Deportivo La Coruna against AC Milan in 2004 and Barcelona against Paris St-Germain last season.
On this occasion, runaway Spanish league leaders Barcelona were on the receiving end of an unthinkable result.
They had no answer to Roma's high-tempo, energetic performance which brought a richly deserved victory.
Ex-Manchester City striker Dzeko, whose former team were knocked out by Liverpool in Tuesday's other quarter-final, set Roma on their way by poking in from close range.
The Bosnia striker also had a header tipped over and Czech forward Patrik Schick nodded wide from a promising position.
Roma, fourth in Serie A, kept up the pressure in the second period and were awarded a penalty just before the hour mark when Gerard Pique bundled Dzeko over in the box and De Rossi despatched the spot-kick.
With time running out, Cengiz Under whipped in a cross towards the near post which Greece defender Manolas rose highest to meet and convert to spark jubilant scenes.
'We don't fear anyone'
Roma striker Edin Dzeko told BT Sport: "It is difficult to believe but we did it and did it in style.
"Nobody believed in us before the game - they gave us a 5% chance of winning - but against such a team like Barcelona, you expect that after losing the first game 4-1.
"We had to be concentrated not to concede a goal. We remembered the first game where they scored four goals from three shots on target as we scored two own goals.
"We believed even more after the first goal - it pushed us and in the end I am so proud.
"The win is difficult to describe. We lost against Fiorentina in the league three days ago but we played an amazing game today and had even more chances to score.
"It was great teamwork from the first to the last minute. It is the first time in history to knock out Barcelona 3-0 and that makes it even more special.
"We will enjoy the semi-finals - I do not fear anyone. They are all top teams. I am just happy to see my team in the draw."
Five-time European Cup winners Barcelona were chasing a treble of trophies this season, having equalled the La Liga record of 38 unbeaten games at the weekend and reaching the Copa del Rey final.
But they were punished for an uncharacteristically poor showing, offering very little in attack and crumbling in the face of the dogged Romans, who were buoyed on by the vocal home support.
Their best chance fell to star player Lionel Messi, but his thumping drive was straight at goalkeeper Alisson and he struck two free-kicks over the crossbar.
It has taken Roma 34 years to reach this stage of the competition, when they were beaten by Liverpool on penalties in the final.
Both sides still remain and could set up a repeat in Kiev on 26 May should they progress.
In Wednesday's remaining quarter-final ties, defending champions Real Madrid are 3-0 ahead against Juventus after the first leg and Bayern Munich lead Sevilla 2-1.
'Underestimate them at your peril' - analysis
European football expert James Horncastle on BBC Radio 5 live
Some say this Barcelona side isn't a vintage one, but still they are still unbeaten in the league. It is an extraordinary achievement for Roma.
People continue to underestimate this Roma side. In the group stages - the group of death with Chelsea and Atletico Madrid - no-one thought they would get through and they topped the group.
The have won every Champions League game at the Olimpico without conceding a goal. That's up against Eden Hazard, Antoine Griezmann, Lionel Messi, Luis Suarez.
Underestimate them at your peril.
Edin into the semis - the stats
- Roma have kept five consecutive clean sheets in five matches at Stadio Olimpico in this season's Champions League, their best run without conceding on home soil in the European Cup/Champions League
- Barcelona conceded as many goals on Tuesday as in their previous 10 Champions League games combined
- Barcelona are without a win in their past five away knockout matches in the Champions League (D1, L5), conceding 13 goals and scoring one
- Edin Dzeko has scored three goals in his past three Champions League games against Barcelona, more than he has netted against any other club in the competition
- Dzeko has scored in three consecutive Champions League appearances for only the second time, and the first since December 2009 with Wolfsburg
- Daniele de Rossi scored his first Champions League goal since bagging a brace against Bayer Leverkusen in October 2015
- 20FazioBooked at 38mins
- 5Nunes JesusBooked at 44mins
- 16De Rossi
- 4NainggolanSubstituted forEl Shaarawyat 77'minutes
- 14SchickSubstituted forÜnderat 73'minutes
- 25da Silva Peres
- 30Santos da Silva
- 92El Shaarawy
- 1ter Stegen
- 2Nélson SemedoSubstituted forDembéléat 85'minutes
- 3PiquéBooked at 57mins
- 5BusquetsSubstituted forAlcácerat 85'minutes
- 8IniestaSubstituted forAndré Gomesat 81'minutes
- 10MessiBooked at 63mins
- 9SuárezBooked at 72mins
- 6D Suárez
- 21André Gomes
- Clément Turpin
- Shots on Target
Second Half ends, Roma 3, Barcelona 0.
Offside, Barcelona. Ivan Rakitic tries a through ball, but Luis Suárez is caught offside.
Foul by André Gomes (Barcelona).
Edin Dzeko (Roma) wins a free kick on the left wing.
Attempt missed. Ousmane Dembélé (Barcelona) right footed shot from long range on the right is just a bit too high.
Attempt blocked. Luis Suárez (Barcelona) right footed shot from the left side of the box is blocked. Assisted by Lionel Messi.
Corner, Barcelona. Conceded by Kostas Manolas.
Ousmane Dembélé (Barcelona) wins a free kick on the right wing.
Foul by Aleksandar Kolarov (Roma).
Attempt saved. Lionel Messi (Barcelona) left footed shot from the centre of the box is saved in the centre of the goal.
Corner, Barcelona. Conceded by Kostas Manolas.
Substitution, Barcelona. Paco Alcácer replaces Sergio Busquets.
Substitution, Barcelona. Ousmane Dembélé replaces Nélson Semedo.
Goal! Roma 3, Barcelona 0. Kostas Manolas (Roma) header from the right side of the box to the bottom left corner. Assisted by Cengiz Ünder with a cross following a corner.
Corner, Roma. Conceded by Samuel Umtiti.
Substitution, Barcelona. André Gomes replaces Andrés Iniesta.
Attempt saved. Stephan El Shaarawy (Roma) right footed shot from the left side of the six yard box is saved in the bottom left corner. Assisted by Alessandro Florenzi with a cross.
Substitution, Roma. Stephan El Shaarawy replaces Radja Nainggolan.
Delay over. They are ready to continue.