This brilliant Bayern Munich side have been bubbling under for some time

Long before the second semi-final kicked off, Europe was still reeling from the events at the Allianz Arena on Tuesday. Kicker magazine described Bayern Munich's 4-0 win over Barcelona as "historic" and Germany certainly woke up this morning with a sense that they might have just seen one of their greatest club teams, and one which is only going to improve.

Maybe it should not be a surprise just how good Bayern are. For some time they have been progressing steadily, making the most of their financial power, buying astutely and developing young players as they forge a team to beat any in Europe. Javi Martinez, who was remarkable in his authority and control in midfield on Tuesday, was last summer's big buy for €40m (£34m) from Athletic Bilbao. Mario Götze is this summer's, joining from Borussia Dortmund for €37m (£31.5m). With Pep Guardiola arriving as coach too, they are only going to get better.

Bayern will now surely make it to the final, where they lost in 2010 and 2012, and if this time they become champions of Europe, it would be a fair reflection of the balance, power, pace and technique of their football.

Like the best teams, it has been the strategic vision and gradual growth of Bayern through those two final defeats to Internazionale and Chelsea which has made them so strong. Their domestic form has been moving in the right direction as well. After missing out on the Bundesliga title to Borussia Dortmund in 2011 and last year, this season they have taken 81 points from a possible 90, making them very comfortable champions indeed.

So the Bayern team which faced Barcelona on Tuesday was certainly on an upswing, just as Barça have been slowly fading since the 2011 Champions League final triumph over Manchester United and the departure of an exhausted Guardiola one year later.

Guardiola will be replacing Jupp Heynckes at Bayern this summer but the veteran German coach still has the spirit and imagination to teach his players the perfect method for overcoming Barça. Heynckes spoke with pride on Tuesday night about his Powerpoint presentation detailing Barcelona's attacking movements and his plans to stop them, and his delight in how his players took his instructions on to the pitch.

Barça have been out-manoeuvred a few times in recent years but this was their worst beating in Europe in a generation. Bayern only had 37 per cent of possession but created 13 goal attempts to Barça's four, nine on target to the Spanish team's two. And those two were weak stabs at goal by Marc Bartra, the young centre-back who looked out of his depth.

When Barcelona lost the 2010 and 2012 semi-finals to Inter and Chelsea respectively, better finishing would have sent them through, and there was also an element of luck involved. Not on Tuesday, when they looked flatter than ever before.

But that is what this talented Bayern side can do to you. They combined the toughest, strongest, most complete engine room in Europe – in Martinez and Bastian Schweinsteiger – with two of the best old-fashioned wingers in Europe, Arjen Robben and Franck Ribéry, and a pair of selfless, intelligent forwards in Thomas Müller and Mario Gomez. Add an imposing centre-back duo, quick full-backs plus a fearless, charismatic goalkeeper and it is quite a team.

Bild wrote that Müller is the "Bayern Messi", but he was far more effective on Tuesday. He is not the most gifted player in the team but has a nose for goal, making sharp runs into the six-yard box to score Bayern's first and fourth on a magical night. The latter went in just in front of a Bayern fans' banner proclaiming "Schöne heile Welt", meaning "Beautiful perfect world". They have been building one for some time in Bavaria. Surely next month, Wembley will see it too.