[2] At the beginning of his musical career, he was a member of Pavel Daněk's band Burčiak and later formed his own group, Banket, with whom he recorded three studio albums.

In the beginning of the 1980s, while studying drama and screenwriting at the Academy of Performing Arts in Bratislava, he started writing for the daily paper and the only specialized periodical at the time, Popular, and later for Gramorevue.

The track found success on the charts, and this encouraged Müller to start his own band, called Banket, which also included Andrej Šeban.

He initially found success singing in Czech, including such songs as "Štěstí je krásná věc" and "Rozeznávám", but eventually switched to his native language.

He released his debut album, Neuč vtáka lietať, in 1992, and followed it in 1994 with 33, his first collaboration with pianist and longtime friend Jaroslav Filip.

[citation needed] In 1995, Müller again worked with Šeban as well as with Oskar Rózsa and Emil Frátrik, on a series of improvisations they called PPF.

[4] Rózsa produced Müller's 2000 album, ...a hosté, which included Šeban on guitar, Filip on piano, as well numerous musical guests from Czechia and Slovakia, such as Ivan Tásler, Michal Horáček, David Koller, Robert Kodym, Anna K, Hana Hegerová, Petr Hapka, and Iva Bittová.

[5] In 2005, he toured Czechia and Slovakia with the backing of drummer Omar Hakim, bassists Anthony Jackson and Will Lee, guitarists Hiram Bullock and Mike Caffrey, and keyboardist Clifford Carter.

Müller has moderated various radio and television shows as well as appearing in a few productions as an actor, including the long-running Panelák, the 1998 film Rivers of Babylon, and 2015's Burácení.