Here, we look at some of their most significant results on the continental stage
April 29, 1970: European Cup Winners' Cup (final), Manchester City 2 Gornik Zabrze 1
The golden era of Joe Mercer, which took City from the Second Division in the mid-1960s to First Division title in 1968 and then FA Cup success a year later, continued with European glory in 1970
City went into the final against their Polish opponents in Vienna without star man Mike Summerbee but prevailed in heavy rain thanks to a Neil Young strike and a penalty from the inspirational Francis Lee, despite a reply from Stanislaw Oslizlo.
November 25, 2014: Champions League, Manchester City 3 Bayern Munich 2
The Etihad Stadium rocked like never before in the Champions League as Sergio Aguero struck twice in the last five minutes to complete a hat-trick and a fine comeback against the 10-man German outfit, then managed by current City boss Pep Guardiola
It was a result that reignited hopes of reaching the last 16 after failing to win their first four group games
City went ahead with an Aguero penalty after Mehdi Benatia was sent off but Bayern replied through Xabi Alonso and Robert Lewandowski
Defeat looked likely until Aguero produced his late heroics to score in the 85th minute and in stoppage time.
December 10, 2014: Champions League, Roma 0 Manchester City 2
City completed their late charge into the knockout stages by winning a testing away fixture in the Italian capital
Samir Nasri broke the deadlock with a superb long-range strike on the hour and Pablo Zabaleta made the result safe four minutes from time
Joe Hart made crucial saves from Gervinho and Kostas Manolas.
April 12, 2016: Champions League, Manchester City 1 Paris St Germain 0
City were already in uncharted territory, having never previously reached the quarter-final stage of the Champions League, before a 2-2 draw away in Paris put them in control of the last-eight tie
In the home leg, Aguero missed a first-half penalty and Hart was again on top form before Kevin De Bruyne's goal 14 minutes from time at the Etihad Stadium sealed a memorable 1-0 win as they progressed to the semi-finals 3-2 on aggregate.
November 1, 2016: Champions League, Manchester City 3 Barcelona 1
This was a sensational performance and result, made all the more remarkable as it came just two weeks after a 4-0 reverse to the same opponents at the Nou Camp
City recovered from conceding an early Lionel Messi goal with two strikes from Ilkay Gundogan either side of a sublime Kevin De Bruyne free-kick
With both sides spurning numerous other chances, it was a thrilling end-to-end contest
It will not only be remembered as a classic for footballing reasons but it could have historical significance as marking the dawn of a new era for City, with the club now looking like they belong among the elite
All that combined may make it City's greatest European night.
Source : PA
Source: PA