The ensemble was founded in 2002, bringing together Dagna Sadkowska (violin), Michał Górczyński (clarinet, bass clarinet), Paweł Nowicki (percussion instruments), and Piotr Nowicki (piano). From the very beginning Kwartludium has focused on performing new music, created especially for its unique instrumental lineup. An important place in the ensemble’s work is also occupied by contemporary improvised music. The ensemble’s repertoire includes graphic and intuitive compositions by leading exponents of new music such as Karlheinz Stockhausen, Roman Haubenstock-Ramati, Bogusław Schaeffer, Cornelius Cardew, and Dubravko Detoni. The ensemble has several dozen Polish and world premieres to its credit, and has given concerts in the United States, United Kingdom, Italy, Belgium, the Netherlands, Germany, Denmark, Finland, Slovakia, Ukraine, Russia, Turkey, Australia, and South Korea. The musicians have appeared at festivals including Warsaw Autumn, Dialogue of Four Cultures in Łódź, Unsound in Cracow and New York, Ensemble Europa in Cologne, C3 in Berlin, Open Form in Copenhagen, Loop in Brussels, Nuove Musiche in Palermo, Contrasts in Lviv, Codes in Lublin, Musica Polonica Nova in Wrocław, Musica Moderna in Łódź, Laboratory of Contemporary Music in Warsaw, Audio-Art and Ad Libitum in Warsaw, New Music Days and Avant Days in Gdańsk. 

In 2007 Kwartludium was awarded a scholarship under the Ministry of Culture and National Heritage’s Young Poland programme. The ensemble has made three recordings released by the DUX label and one, in cooperation with Michał Jacaszek, released by the British label Touch. In 2015 Requiem Records released Hammond Project, a recording made by the ensemble with the organist and composer Dariusz Przybylski. In 2009 Kwartludium, alongside 21 of the most interesting ensembles specialising in contemporary music, took part in a prestigious European project, Re:New Music, promoting selected European composers. In 2012 the ensemble was invited to join another European programme, New Music:New Audiences.