Celtic belied their mediocre domestic form in Scotland by reaching the semi-final of the tournament, eliminating Basel, Dinamo Zagreb and Slovan Bratislava en route.

At chairman Robert Kelly's behest, the club sent UEFA a telegram condemning the military action and expressing concern that any team from Western Europe having to play a tie in an Eastern Bloc country.

[39][42] The return match was played at Hampden Park on 15 April 1970 in front of 136,505 spectators,[43] a record attendance for a competitive European club tie that stands to this day.

[43] Jimmy Johnstone had a particularly outstanding match[43][44] and his mazy run set up Bobby Murdoch to score with a powerful shot,[44] sealing a 2–1 win for Celtic on the night and their progression to the final.

Feyenoord manager Ernst Happel ensured Jimmy Johnstone was double marked at all times, while the midfield trio of Franz Hasil, Willem van Hanegem and Wim Jansen dominated their Celtic counterparts.

Before the referee had a chance to award a penalty, Ove Kindvall reacted quickly and took the ball around his man before chipping it over goalkeeper Evan Williams to seal a 2–1 win for Feyenoord.

[48][49] In the buildup for the second leg in Spain, Jimmy Johnstone received a death threat over the hotel phone[49] and a hate campaign from the Spanish media prevented the Celtic players from relaxing or training effectively.

[58] Goalkeeper Peter Latchford had an excellent match, and in particular his saves from England striker Laurie Cunningham and Spanish star Santillana were crucial in helping Celtic keep a clean sheet.

Uli Stielike levelled the tie in the second half with a powerful volley past Latchford, before Juanito added a third near the end to send Celtic out 3–2 on aggregate.

The first leg in Glasgow saw Ajax twice take the lead through goals from Jesper Olsen and Søren Lerby, but Celtic responded with strikes from Charlie Nicholas and Frank McGarvey to draw 2–2 on the night.

[74] The return match at Parkhead was an even more bad-tempered affair as Celtic raced to a 3–0 lead with goals from Brian McClair, Murdo MacLeod and Tommy Burns, all in spite of Rapid's foul play.

Mo Johnston's headed goal from a Davie Provan cross and Pat Bonner's late penalty save from Juan Jose Rubio secured a 1–1 draw away in Madrid, putting Celtic in a good position to win the tie.

Celtic recovered from a 2–0 first leg defeat away at Cologne in the UEFA Cup to win the return match in Glasgow 3–0, midfielder John Collins scoring the decisive third goal seven minutes from time.

A credible performance at home in the first leg resulted in a 1–0 win, Creaney controlling a Paul Byrne pass with his chest on the edge of the penalty area and scoring with a powerful shot.

With the match going into injury time and the tie poised on a knife edge, Larsson went on a solo run forward, beating several tackles, before passing to Burley who scored from close range to clinch a 6–3 win on the night to progress on aggregate.

With full-time approaching, Steve McManaman picked the ball from inside his own half, dribbled 70 yards to the edge of the Celtic penalty box and curled a shot to level the match at 2–2.

[137] Celtic played poorly in the first leg at Parkhead, but a Henrik Larsson goal six minutes from full-time secured a crucial 1–0 win on the night and a narrow lead to take down to Ewood Park.

Alan Thompson struck a low shot past Jerzy Dudek from the set piece, with the ball going under the defensive wall which had jumped up and appeared to distract the Liverpool goalkeeper.

Celtic sealed a 2–0 victory on 82 minutes when John Hartson played a one-two with Larsson, then drove a swerving shot from 25 yards out into the top-right corner of Dudek's goal.

A dramatic first leg in Glasgow saw Celtic win 1–0 through an Alan Thompson goal, but goalkeeper Rab Douglas and Barcelona's Thiago Motta were sent off during half-time for fighting in the tunnel.

[160] The return match in Spain saw Celtic fielding 19-year-old reserve goalkeeper David Marshall in place of Douglas and young defender John Kennedy standing in for Bobo Baldé, who was also suspended.

[164] Gordon Strachan made an unpromising start as manager of Celtic in the summer of 2005, losing his first match in charge – a Champions League qualifier – 0–5 to Slovakian side Artmedia Bratislava, the club's worst ever European result at that time.

[182] As such, an "Ultras"-styled section of the Celtic support called the Green Brigade organised a full stadium pre-match card display (a "tifo") to celebrate the club's 125th anniversary.

[185] Goalkeeper Fraser Forster produced an outstanding performance in the game, winning the praise of the Spanish media who nicknamed him "La Gran Muralla" ("The Great Wall").

[198] Ronny Deila's first competitive match in charge of Celtic was a Champions League qualifying tie away against KR Reykjavik on 15 July 2014, which ended in a 1–0 win with midfielder Callum McGregor scoring the decisive goal on 84 minutes.

[210] Celtic's first competitive match under new manager Brendan Rodgers, saw the team lose 1–0 against Gibraltarian minnows Lincoln Red Imps in the first leg of the Second Round 2016–17 Champions League qualifiers, a result described by The Scotsman as a "humiliation".

[218][219][220] Celtic gained only three points over the six games with a 3–0 away win – their first European group stage victory in 16 attempts – at Anderlecht,[221] and finished in third place despite losing 5–0 and 7–1 to Paris Saint Germain.

[230] Rosenborg helped Celtic to qualify from the group despite the Scottish champions losing at home to Salzburg; the Norwegians scoring a late equalizer against Leipzig in Germany which put the Hoops ahead on points when they had been behind the German side on the tiebreak methods.

[232] The early rounds of the 2019–20 Champions League qualifying phase saw Celtic ease past FK Sarajevo and Nõmme Kalju with comfortable aggregate victories.

As of January 2020, Henrik Larsson is the all-time joint eleventh top goalscorer in European club football competitions with a total of 59 goals from his time at Feyenoord, Celtic, Barcelona, Manchester United and Helsingborgs IF.