Match ends, Monaco 3, Manchester City 1.
Manchester City are out of the Champions League after Monaco struck late to seal a thrilling away-goals victory, which ended 6-6 on aggregate.
The English side were 13 minutes from a place in the quarter-finals after clawing themselves back into a second leg their hosts had dominated, but slack marking from a set-piece allowed Tiemoue Bakayoko to head home the decisive goal.
Having won the competition twice in his time at Barcelona, this is the first time in manager Pep Guardiola's career that he has gone out at this stage.
Monaco lost 5-3 in an extraordinary first leg in Manchester but dominated the first half at the Stade Louis II and opened the scoring through the excellent Kylian Mbappe's poked finish from close range.
The Ligue 1 side, who had scored 123 goals so far this season, deservedly doubled their advantage on the night, punishing City's sluggish start through Fabinho's crisp strike.
City failed to muster any sort of shot in the opening 45 minutes and it took until the 65th minute for Sergio Aguero to call goalkeeper Danijel Subasic into a sharp save.
They forced their way into the game - and back into the aggregate lead - as Leroy Sane swept in when Subasic parried Raheem Sterling's low strike, but their defence could not hold out.
The result leaves Premier League champions Leicester City as the only English team in the last eight.
Monaco join the Foxes, holders Real Madrid, last year's runners-up Atletico Madrid, Barcelona, Bayern Munich, Borussia Dortmund and Juventus in Friday's draw.
- 'I couldn't convince them to attack' - Pep says he takes the blame
- Listen: 'Man City have failed to live up to expectations' - Phil Neville
- Relive Monaco's brilliant victory
Guardiola gets it wrong
Having gained a two-goal advantage at home, City boss Pep Guardiola had vowed his side would go on the attack in order to finish the job.
But while the Spanish coach can boast the best record of any manager in Europe after 100 games, he opted to start with only Fernandinho in the middle of the park against the aggressive and youthful French side.
Five attack-minded players were deployed in front of the Brazilian midfielder, while Yaya Toure was left on the bench, and it proved a costly move as City were overrun by sharper opponents.
Although they pulled a goal back on the night through Sane - putting them briefly back in front in the tie - the English side never recovered from their poor first-half showing.
Big-money signing John Stones struggled again and Monaco's winning goal epitomised the fragility of the visitors' defensive backline, as the impressive Bakayoko was allowed a free header eight yards from goal.
Guardiola has said his maiden City season will be a failure if he cannot deliver a trophy, but barring a dramatic Chelsea collapse in the Premier League, the Spaniard's only realistic hope of silverware is now the FA Cup.
The City boss made some unwelcome history in France as his side became the first team to be eliminated in a Champions League knockout tie after scoring five goals in the first leg.
French youngsters show their class
The Ligue 1 leaders were missing star striker Radamel Falcao, who had failed so spectacularly in England with loan spells at Manchester United and Chelsea.
But the home side took the game to City, allowing them little time and space on the ball, forcing errors and taking their chances superbly. Although they began to tire in the second half, the 2004 runners-up managed to edge through.
Eighteen-year-old striker Mbappe - who has earned comparisons to retired France great Thierry Henry - found the net after just eight minutes for his 17th goal of the season, fed by the brilliant Portuguese midfielder Silva.
Benjamin Mendy caused all sorts of problems by bombing on from full-back, but man of the match Bakayoko deservedly took his side through with the winning goal.
The towering France Under-21 international controlled the midfield and gained possession nine times - more than any team-mate.
Former Manchester United defender Phil Neville on BBC Radio 5 live:
They have been two brilliant football matches. City lost it in the first half when they were outplayed, outfought and were bullied.
They got back into the game and they thought they were through. But their Achilles heel was a sloppy goal. Another year has failed to live up to expectations.
I am not so sure the signings over the last five years have been that good, but when Leroy Sane scores, Pep Guardiola is thinking 'this is perfect, we can control the game from here'. Then they concede.
Guardiola doesn't go out there and spend the bulk of his money on defenders. He will be thinking if they had put one of those chances away they would be in the next round.
'Sometimes you have to be lucky'
Manchester City boss Pep Guardiola, talking to BT Sport: "We played exceptional second half but we forgot to do that in the first. We wanted to defend aggressively. We were better in the second but it wasn't enough.
"Normally we play to a good level but here we didn't. We will learn. The team does not have a lot of experience.
"The second half we had the chances and we didn't take them and that is why we are out. And set-pieces are so important at this level. Barcelona and Real Madrid scored from them last week. We were not there and we were not there in the first 45 minutes.
"We will improve but this competition is so demanding. Sometimes we have to be special and be lucky. We were not."
City's defensive frailties - the stats
- Monaco have progressed from all four of their Champions League knockout ties against English teams.
- David Silva played his 50th Champions League game, becoming the 25th Spaniard to reach that milestone in the competition.
- Kylian Mbappe has scored 11 goals in his past 11 games in all competitions.
- Bernardo Silva has provided an assist in each of his past three games for Monaco in all competitions.
- City are without a clean sheet in their past 11 away games in the Champions League (excluding qualifiers).
- The English side failed to muster a single shot in the first half of a Champions League game for the first time.
- Fabinho has had a hand in three goals in two Champions League appearances versus Manchester City this season (one goal, two assists).
- Leroy Sane scored with just his 11th shot on target for City this season (all competitions).
- 24RaggiSubstituted forTouréat 70'minutes
- 10Bernardo Silva
- 14BakayokoBooked at 59mins
- 27LemarBooked at 90mins
- 18GermainBooked at 89minsSubstituted forDirarat 90+1'minutes
- 29MbappeSubstituted forJoão Moutinhoat 81'minutes
- 6de Oliveira Moraes
- 8João Moutinho
- 16De Sanctis
- 3SagnaBooked at 11mins
- 22ClichySubstituted forIheanachoat 84'minutes
- 7SterlingBooked at 74mins
- 17De BruyneBooked at 58mins
- 42Y Touré
- Gianluca Rocchi
- Shots on Target
Second Half ends, Monaco 3, Manchester City 1.
Thomas Lemar (Monaco) is shown the yellow card for a bad foul.
Kevin De Bruyne (Manchester City) wins a free kick in the attacking half.
Foul by Thomas Lemar (Monaco).
Substitution, Monaco. Nabil Dirar replaces Valère Germain.
Valère Germain (Monaco) is shown the yellow card for a bad foul.
Aleksandar Kolarov (Manchester City) wins a free kick in the attacking half.
Foul by Valère Germain (Monaco).
Foul by Kevin De Bruyne (Manchester City).
Fabinho (Monaco) wins a free kick in the defensive half.
Foul by Fernandinho (Manchester City).
Valère Germain (Monaco) wins a free kick on the right wing.
Substitution, Manchester City. Kelechi Iheanacho replaces Gaël Clichy.
Offside, Manchester City. David Silva tries a through ball, but Leroy Sané is caught offside.
Sergio Agüero (Manchester City) wins a free kick in the attacking half.
Foul by Jemerson (Monaco).
Substitution, Monaco. João Moutinho replaces Kylian Mbappe.
Leroy Sané (Manchester City) wins a free kick on the left wing.
Foul by Djibril Sidibe (Monaco).