But for ASM Clermont Auvergne, Montpellier, Saracens, Harlequins and Toulon the lure is to have their name etched onto the trophy for the first time.
Here are some quarter-final milestones ….
• Montpellier are appearing in the quarter-finals for the first time in only their second season in European club rugby's elite tournament.
• The 2013 quarter-finalists have 36 quarter-final appearances between them.
• Munster are appearing in a record 14th quarter-final - and they have won nine of them.
• The 64 Heineken Cup quarter-finals have been watched by 1,436,989 fans with an average attendance for each of the quarter-finals of 22,453.
• The 55,000 who packed into Barcelona's Olympic Stadium for the 2011 quarter-final between Perpignan and Toulon was a record crowd for a Heineken Cup quarter-final.
• Only one of the 64 quarter-finals has required extra time to establish a winner - the 2011 all-French contest between Biarritz Olympique and Toulouse, with four-time champions Toulouse finally going through 27-20 after 100 minutes of action.
• Ulster Rugby and ASM Clermont Auvergne won on the road in last season's quarter-finals with 48 of the 64 quarter-finals ending in home wins. There was not a single away win in sight in the three successive tournaments between 1998/99 and 2000/01 and again in 2010/11 while Munster account for three and Toulouse for two of those 16 away triumphs.
• There have been only three try hat-tricks in the quarter-finals - an average of just under one in every 20 matches - scored by Anthony Foley for Munster against Biarritz Olympique (2001); Olivier Sarramea for Stade Français Paris against Newcastle Falcons (2005) and Julien Malzieu for ASM Clermont Auverge against Leinster (2010).
• Cardiff Blues and Leicester Tigers were involved in the only penalty shoot-out so far required to decide the winner of a Heineken Cup knock-out match. Leicester won the 2009 deadlocked Millennium Stadium semi-final 7-6 on penalties.
• Damien Traille, the Biarritz Olympique centre, kicked a tournament quarter-final record of three drop goals in the 29-28 victory over the Ospreys in 2010.
• Munster prop John Hayes appeared in a record 12 quarter-finals before hanging up his boots - one more than former team-mates Peter Stringer and David Wallace.
• The 2004 / 2005 quarter-finals had the greatest combined attendance of 162,500 - an average of over 40,000 per quarter-final - when the ties were played at Lansdowne Road (Leinster v Leicester Tigers), Estadio Anoeta (Biarritz Olympique v Munster), Parc des Princes (Stade Français Paris v Newcastle Falcons) and Le Stadium in Toulouse (Toulouse v Northampton Saints).
• There were no quarter-finals in the first season of the tournament, the four Pool winners going straight into the semi-finals.