It is a club that has since struggled in Europe, though there have been recent flickers of life with Europa League and Conference League campaigns, with the most recent in the latter producing knock-out European tournament football.
Like Celtic, Slovan have been the dominant force at home, winning each of the last six Slovakian titles with a 16-point chasm between they and nearest challengers Zilina last season.
They are top of the embryonic Fortuna Liga table this season despite suffering a spectacular 5-0 home thrashing by last term’s runners-up before the September international break.
As far as Champions League fixtures go, Celtic may never have had a better chance to win their opening game of the tournament proper for the first time since its 1990s rebrand.
Slovan are strong at home, but this is the first time they have qualified for the Champions League at the 12th time of asking.
They are one of five tournament debutants in the new-look competition, and at a full Celtic Park under the lights, it would be a major blow if the Scottish champions don’t win this game and boost their own hopes as well as the flagging Scottish co-efficient.
It was a marathon qualification campaign for Slovan to even reach this point.
Vladimir Weiss’ side emerged from four ties, beating the Danish champions Midtjylland in the play-off to finally make the leap onto the big stage.
Weiss – who is hoping to overcome a virus to make the trip to Glasgow – has previous when it comes to shocking Celtic having been in charge of Artmedia Bratislava when they infamously ruined Gordon Strachan’s bow at the club in 2005.
Strachan had just replaced Martin O’Neill and despite their second-leg heroics, the 5-0 loss in Slovakia saw them knocked out of Europe altogether.
Weiss’ son Vladimir junior had a profitable loan at Rangers in the 2010-11 season, setting up Nikica Jelavic for the winning goal in the League Cup final against Celtic. He will be hoping to get the chance to renew acquaintances in his final campaign before retirement.