All major phases of Schoenberg's career are represented in the four quartets, except for his mostly explicitly Expressionist phase, 1909-1922. For him, the string quartet was inextricably associated with substantial four movement structure and classical form, and therefore grew naturally out of the resources either of major-minor tonality or later via the method of composing with twelve tones. Thus, the four quartets embody a broad range of expressive and compositional motivations, but ultimately show Schoenberg reaching back to a genre with strong associations to the established Austro-German repertoire extending from Haydn to Brahms.

Founded in Los Angeles in 2022, the Webern Quartet has been featured in The New Yorker, where they were praised as having "found the through line of Schoenberg's personality." The Webern Quartet chose the name of Anton Webern, former student of Arnold Schoenberg, whose important string quartet oeuvre has been the starting point of the quartet. In 2023, the Webern Quartet held an extensive residency at the Arnold Schoenberg Center in Vienna where they performed the complete Schoenberg quartets at two concerts on the same day.