Vilém Vlček received his first cello lessons at the age of six with Prof. Martin Skampa. In 2010 joined the class of Martin and Mirko Skampa at Music Gymnasium in Prague. Since 2018 he is student of Danjulo Ishizaka on the Musik-Akademie Basel. He has participated in masterclasses of Yo-Yo Ma, Leonidas Kavakos, Steven Isserlis, Frans Helmerson, Richard Aaron, Alisa Weilerstein and others.

He played as a soloist with many renowned orchestras such as Czech Philharmonic, Kammerorchester Basel, Prague Symphony Orchestra, Luzerner Sinfonieorchester, Kaunas Symphony Orchestra, North Czech Philharmonic, Zielona Gora Philharmonic, Württemberg Philharmonic Orchestra and cooperated with such conductors as Jiri Belohlavek, Jonathan Bloxham, Petr Altrichter, Wolfgang Emanuel Schmidt, Jirí Rozen, Nicolas Ellis and many others.

His soloistic engagements brought him performances in some of the worlds most prestigious venues such as Chamber music hall of the Berliner Philharmonie, the Great Hall of Elbphilharmonie, Tonhalle Zurich, Dvoraks Hall of Rudolfinum, Victoria Hall etc.

Since august 2016 he has been member of LGT Young Soloists and in the 2021-2022 season he was member of the Kukal Quartet.