Violinists Agata Szymczewska and Robert Kowalski, violist Volodia Mykytka, and cellist Monika Leskovar joined forces in Warsaw in 1995 and have continued to be based there despite several residencies abroad. They studied in Hannover, Germany, at the University of Music and Drama with Hatto Beyerle and went on for master classes with Isaac Stern, Walter Levin, and the Juilliard, Emerson, Amadeus, and Guarneri quartets. A major breakthrough in their career was designation as New Generation Artists by the BBC in 2001, for a three-year term. At the end of that period, the quartet released a BBC recording of quintets by Brahms and Mozart. Since then it has issued more than ten recordings on various labels, including SWR Music in Germany, CAvi-music, Hyperion, Decca, and Haenssler. These have included several prominent recordings of Russian music in addition to Polish selections. For CAvi, the quartet has made a series of three recordings of the quartets of Karol Szymanowski himself, focusing on his work in the contexts of Paris, Vienna, and Moscow. Its concert performances are noted for featuring contemporary music, including works by Krzysztof Penderecki, Sofia Gubaidulina, Magnus Lindberg, Myroslav Skoryk, and others, with several new works dedicated to the quartet. It has often toured Poland and Germany, and its 2018 performances included a debut concert at London's Wigmore Hall.
The Szymanowski Quartet received the Szymanowski Award in 2005 from the foundation perpetuating the work of its composer namesake; it was the first string quartet to win the award. In 2007 it was given a medal of honor for services to Polish culture by Poland's government. The following year it founded the Lviv Chamber Music Festival in that historic city, a UNESCO World Heritage site on the Polish-Ukrainian border.