By contrast Edinburgh Rugby are appearing in only their second quarter-final although this time they will have both home advantage and the honour of staging the first tournament knock-out match on Scottish soil. They became the first Scottish club to top a Pool and now the target is to be the first team from Scotland to qualify for the semi-finals.
This will be the 12th tournament meeting between the clubs, with Toulouse 10-1 ahead, but Head Coach Michael Bradley is adamant that home advantage will be a huge boost as his side prepare for what will be the biggest ever Scottish club game with over 31,000 tickets already snapped up.
A host of stars from the two clubs featured in the 2012 RBS 6 Nations - nine from each club, including national captains Ross Ford and Thierry Dusautoir - with the French players admitting they were fortunate to walk off 23-17 winners back in February.
However, there have been sharply contrasting fortunes on the club front this season, Toulouse four points clear at the head of the Top 14 while Edinburgh are down in 11th place in the Pro12. It will also be the 125th game in the tournament for Toulouse - and their remarkable head coach Guy Noves
Both clubs go into the high profile match on the back of domestic victories, Edinburgh beating the Scarlets and Toulouse accounting for Stade Français Paris, but now the prize is a semi-final place on the weekend of 28/29 April against either Munster Rugby or Ulster Rugby.