Zwiebel Quartet was established in a fall 2001 at the field of the Academy of Performing Arts in Bratislava, where all its members studied chamber music (Mária Karlíková). From what was originally student enthusiasm for playing in quartet, its members over time decided to continue as professionals.

In 2002 during the international summer academy Prag – Wien – Budapest it received prestigious Prize Thomastik–Infeld for the interpretation of the Shostakovich Quartet. The ensemble attended several master coursesunder the leadership of members of significant string quartets (Hagen Quartet, Alban Berg Quartet, Bartók Quartet, Smetana Quartet, Amadeus Quartet, Quartuor Mosaiques). Since November 2007 the quartet studied in Basle (Switzerland) at the prestigious semester course for string quartets with Walter Levin (LaSalle Quartet) and Reiner Schmidt (Hagen Quartet).

The quartet presented itself mainly by interpretation of contemporary music and its members were the main support for major festivals of contemporary music in Slovakia, but also abroad (Melos Ethos, New Slovak Music, Ostrava Days and others). It regularly performed in the Slovak Radio in concerts of “Štúdio mladých” (Youth Studio). It cooperated with the association of young composers “Soozvuk”, where in addition to the works of their contemporaries it performed also composition of the older generation. In 2005 the quartet started cooperation with the composition class of Professor M. Jarrell in Vienna at the Universität für Musik und Darstellende Kunst and in the same year it successfully presented itself in a separate recital in Bratislava Music Days (after a long time was once again in Slovakia heard the music of Bartók's Fourth Quartet but also a premiere of the string quartet Dolcissimma mia vita by Juraj Hatrík). In 2005 at the Melos Ethos festival Zwiebel Quartet very successfully performed the Slovak premiere of the composition Different Trains by Steve Reich (in the presence of the composer). Within the Year of Slovak Music (2006) the quartet recorded two string quartets by Ján Levoslav Bella. The ensemble cooperated with personalities such as Zsolt Nagy, Paul Messina, Dave Seidel, Gavin Bryars, Marcel Štefko and others. At the Bratislava Music Days in 2008 the quartet performed the separate chamber concert of works by American composers of 20th century (Osvolio Giolov, Steve Reich, George Crumb). Members of Zwiebel Quartet were at the same time members of the Slovak Chamber Orchestra of Bohdan Warchal and Quasars Ensemble. The ensemble has since disbanded.