The Hoops became the first British club to lift the European Cup in 1967 when they defeated Italian cracks Inter Milan 2-1 in Lisbon.
And that was not the only occasion the Parkhead club has taken on and beaten one of the finest clubs on the continent.
Far from it. The Glasgow giants have regularly defeated the cream of Europe since then. Indeed, just two seasons ago, they conquered Spanish superstars Barcelona in the Champions League en route to qualifying for the knockout stages of that tournament.
The Glasgow giants have also excelled in Scotland over the years.
They have won the Scottish title on 45 occasions, the Scottish Cup 36 times and the League Cup 14 times.
With so many great games and incredible victories, it is nigh on impossible to decide what their 50 most memorable matches are.
But Ronnie Cully and Matthew Lindsay have sifted through back issues of the Evening Times in an attempt to do so.
And today in SportTimes we begin the countdown of their most exciting, most significant and most improbable results in the last 70 years.
Not every Celtic fan will agree with the matches they have come up with - or the order they have put them in. But they will enjoy looking back on all of their club's most memorable moments ...
Game: Celtic v Atletico Madrid.
Date: Wednesday, October 2, 1985.
Competition: European Cup-Winners' Cup.
Venue: Celtic Park.
Result: Celtic 1 Atletico Madrid 2.
The most bizarre game ever staged at Celtic Park, because it was played behind closed doors.
The shut out was part of the harsh punishment the Hoops were handed by Uefa for the problems during the previous season's infamous games against Rapid Vienna at Parkhead and in the replayed match at Old Trafford.
It was ironic Atletico should be the club to provide the opposition, given their shocking behaviour on their previous visit.
Having managed to earn a 1-1 draw in the first leg in Madrid, Davie Hay's side felt confident going into the home leg.
But Setion and Quique put Atletico 2-0 up midway through the second half, and Roy Aitken's counter was not enough to save the tie.
GAME: Dundee v Celtic.
Date: Saturday, April 17, 1948.
Competition: League Division A.
Venue: Dens Park.
Result: Dundee 2 Celtic 3.
It was more relief than celebration for the Hoops after this win as they had travelled to Dens for the final game
of the campaign facing the real possibility of relegation from the A Division established after the war.
Having won just nine of their previous 29 matches, they needed a victory to be sure of survival.
Jock Weir was the hero of the day, scoring all three goals to take the points which saw the Hoops finish fifth from bottom of the 16-team league.
They had trailed 2-1 after Ewen and Mackay cancelled out Weir's early opener.
But the Hoops finished strongly, with the pressure-relieving winner coming two minutes from time.
Game: Celtic v Feyenoord.
Date: Wednesday, May 6, 1970.
Competition: European Cup final.
VENUE: San Siro, Milan.
Result: Celtic 1 Feyenoord 2 (aet).
IT seems incongruous a European Cup final appearance should not rank higher among Celtic's greatest games, but the result - and the performance - dictates its position.
The Hoops should have been crowned European champions for the second time in three years, but complacency undermined their advantage over their Dutch opponents.
Jock Stein was guilty of believing the trophy was Celtic's after he had masterminded the semi-final victories over Leeds.
All appeared to be going to plan when Tommy Gemmell opened the scoring after half an hour - how many other full-backs can boast they scored in two European
Although Rinus Israel hit back, Celtic looked as though they could take the game to a replay, but Ove Kindvall scored the winner four minutes from the end of extra-time.
GAME: Rangers v Celtic.
Date: Saturday, March 22, 1986.
Competition: Premier League.
Result: Rangers 4 Celtic 4.
All that is great about Old Firm games was delivered in 90 pulsating minutes in appalling conditions.
The teams shared eight goals, and the fans were treated to a ding-dong battle.
Mo Johnston and Brian McClair fired the Hoops ahead in the first half before Willie McStay was shown red on 33 minutes by referee Davie Syme.
Cammy Fraser scored to bring Rangers back into it by half-time, but Tommy Burns got Celtic's third two minutes after the break.
Ally McCoist, Robert Fleck and Fraser again all scored within an 11-minute burst to finally put the home side ahead.
But Murdo MacLeod saved the best for last, blasting in the equaliser from 30 yards to send every one of the fans home feeling like a winner.
Game: Rangers v Celtic.
Date: Saturday, May 14, 1983.
Competition: Premier League.
Result: Rangers 2, Celtic 4.
This Old Firm game was made memorable, not because of the significance of the result - Celtic still finished second to Dundee United in the championship by a point - but because the Hoops came from 2-0 down at half-time to win. Goals from Davie Cooper and Sandy Clark appeared to have put a shine on what had been a poor season
But Billy McNeill's side came out fighting after the break. And two penalties from Charlie Nicholas - yes, they were awarded two penalties at Ibrox - in his final game for the club, either side of headed goals from Tom McAdam and Frank McGarvey, capped a remarkable comeback.
Your Shout ...
Now it's your turn to let us know what you think about Celtic's 50 most memorable matches. Get in touch via email at email@example.com and have your say on the Hoops' biggest-ever games.