GLASGOW Warriors have come a long way over the past few years: Saturday’s extraordinary demolition of Leicester was proof of that. But if they are to achieve the ultimate goal of winning the Champions Cup and not just reaching the quarter-finals, it may be that they have just as far to travel again.

That does not necessarily mean they will need a set number of years before they take the next two steps, into the semi-finals then the final itself. They made that kind of gradual progress in the PRO12, advancing little by little before eventually winning the final in 2015, but that was more about accruing experience of how to handle big-match occasions. They have that experience in their armoury now.

Instead, they probably have to make two significant changes to their game plans and their ability to deliver them tactically. This will in part be down to key players within the squad maturing and becoming more consistently excellent, but it may also rely on new signings introducing greater versatility.

The first change is learning how to cope with teams such as Munster who like to asphyxiate the life out of a match. The Warriors have beaten Munster in the past, of course, most memorably in that 2015 final, so making the step up is within their grasp. Indeed, they have already made significant progress in that regard, as Gregor Townsend pointed out after the weekend win at Welford Road.

There was a time when, if Glasgow wanted to get the better of forward-dominated opponents such as Leicester, they had to steer the play away from the pack as much as possible. The backs did not quite have to live off scraps, but the team did need to keep the ball moving rather than trying to get the better of a grinding game based around the set piece.

That has long been a necessary policy for lighter, nippier Scottish teams when finding themselves in a catchweight contest. But on Saturday, not for the first time, Glasgow gave as good as they got - and then some more - against the Tigers.

Jonny Gray has become a vital leader in this increasingly successful battle, to the extent that we are tempted to take his massive contribution for granted. But over the past couple of weeks he has been equalled by his second-row partner Tim Swinson, whose drive and distribution against Munster was one of the principal reasons that the Warriors remained in that match for so long before going down to a 14-12 defeat. And in the back row, the indomitable Ryan Wilson’s energy and enthusiasm at times make him look like a real glutton for punishment - even if it is usually his opposite number who ends up being punished.

“Two years ago we lost at Bath,” Townsend, the Glasgow coach, said on Saturday night. “We scored two outstanding tries that day and played ambitious rugby, but we weren’t good enough in the set piece. We made big improvements in that area and I thought our set piece was outstanding here.”

It was indeed, but you suspect that at times it is the desire of Townsend’s team to play ambitious rugby that still makes them vulnerable to sides such as Munster. If your first instinct is to run the ball, to express yourself and entertain the support, you can be picked off by teams who are more willing to play a dour game.

As the final score suggests, the Warriors came close to beating Munster in that last meeting at Scotstoun, but the fact remains that they have lost to the Irish province three times this season. However, getting the better of them will not need much of a change - and perhaps will be down to no more than a couple of decisions at critical stages of the match.

Leicester are clearly going through a difficult time at the moment, which means beating them so comprehensively cannot allow us to presume that on the same form Glasgow would also have beaten Munster. But the versatility shown in that win, particularly the ability to switch instantly from a pick-and-go, gradual-gain approach in attack to a lightning-fast coup de grace, is the kind of thing that will be needed if they are prevail over opponents who offer more solid, less demoralised resistance than the Tigers did.

If and when that change is effected, the second improvement, when faced with the best teams on the continent, will have to be to become even more devastating in attack. We should not forget that Glasgow have lost some of their best attackers in recent seasons, and that this first-ever qualification for the last eight in Europe has been achieved in the face of that significant depletion of resources. Is it too much to hope that, when Dave Rennie takes over from Townsend for the start of next season, he will be given the funds to make one or two key signings?

If you look at the on-field strength and off-field purchasing power of teams such as Saracens, their quarter-final opponents, it is clear that the Warriors will need to punch above their weight to go through to the last four. We should be proud of what they have achieved already, and the style with which they have done so. We will be prouder still if they took those next two steps and go on - if not this season, in the three or four to come - to be crowned champions of Europe.