Edinburgh came closest to lifting the precious prize, losing in 22-19 to Ulster in the 2012 semi-finals.
The tournament’s winners have been drawn from three nations, with English clubs coming out on top with ten triumphs. France are next with eight victories, and Ireland are just behind with seven.
Wales, like Scotland, have yet to taste success in European rugby’s top club competition but they can at least boast a finalist - Cardiff, in the augural 1995-96 competition when they lost to Toulouse.
So, can a Scottish team win it?
“Yes,” says Danny Wilson, whose Glasgow Warriors side face the toughest of opening matches against holders Exeter away tomorrow.
“That’s what we’re all in this for, isn’t it? We’re in it to challenge and win. We all want to be part of winning trophies. Those big days are what all the hard work and going through all that pain is for.
“It is certainly a challenging year, as we know, but I think we go into any competition with the ambition to win – and on this occasion we start off playing the best team in last year’s competition. So, we’ll soon find out – it’s a big test.”
History shows that Glasgow have no reason to be frightened of Exeter, having won three times and drawn once in six Champions Cup meetings with the Devon club.
But the Warriors have lost a number of big players in recent seasons, with two of them, Stuart Hogg and Jonny Gray, joining the Chiefs who have built assiduously under coach Rob Baxter to become champions of England and Europe,
“They’ve got some pretty good boys there,” admitted Wilson. “I think they’ve built a very deep squad over a period of time. Rob Baxter has been there for a long, long time.
“I coached against him in the Championship many years ago, and they’ve just built and built and built. They have been very well financed and backed, as we know, and they’ve built to a position where they can go out and sign the likes of Hoggy and Jonny.
“They built it the hard way. Not with massive budgets, but with a lot of local talent identification in a hotbed of rugby down there, and they’ve brought a lot of people through the club who have gone from the Championship, into the Premiership, into qualifying for Europe, and ultimately winning in Europe – so it is quite a story.”
As expected, Wilson has rung the changes for Europe and brought back eight Scotland players into his starting XV. With the international window finally over, Glasgow are bolstered by the addition of Oli Kebble, George Turner, Zander Fagerson, Scott Cummings, Matt Fagerson, Ali Price, Sam Johnson and Nick Grigg.
“A huge chunk of players has come back in and it has raised the standard of training and raised the noise and the leadership,” said Wilson.
One notable absentee is hooker and co-captain Fraser Brown who misses out with a shoulder and neck injury.
Tomorrow’s match will see the return of fans at Sandy Park, with 2000 Exeter season-ticket holders permitted entry. A welcome first step on the return to normality for rugby.