The playing of the Takács Quartet tends to inspire superlatives: "The Takács Quartet is universally recognized as one of the world's finest string quartets," "The Takács might play this repertoire [the Beethoven quartets] better than any quartet of the past or present," "They are currently the greatest string quartet in the world." The group's international performances have continued to bring accolades, and recordings have been recognized with numerous awards.

The group was formed in 1975 when its members were students at the Franz Liszt Academy in Budapest. The original quartet consisted of violinists Gabor Takács-Nagy and Károly Schranz, violist Gabor Ormai, and cellist András Fejér. There have been several changes in personnel, but Fejér remains a member. Edward Dusinberre replaced Takács-Nagy when he retired from the group in 1992. Ormai died in 1995 and was replaced by Roger Tapping. In 2005, Tapping retired, and Geraldine Walther took his place. Schranz retired in 2018 and was replaced by Harumi Rhodes. The quartet quickly rose to prominence, winning First Prize and the Critics' Prize at the 1977 International String Quartet Competition, and the Gold Medal at the Portsmouth and Bordeaux Competitions in 1978.

The Takács Quartet has ventured into the contemporary repertoire, playing works by composers such as Henri Dutilleux, Bright Sheng, James MacMillan, and Wolfgang Rihm, but for the most part has concentrated on the core quartet literature: Haydn, Mozart, Beethoven, Schubert, Brahms, Dvorák, and Bartók. The quartet's recording of the complete Bartók quartets earned the group a Gramophone Award in 1998. The most ambitious recording project has been the complete quartets of Beethoven, which were released on Decca between 2002 and 2004. It received a Grammy and two Gramophone Awards for a recording of the Rasumovsky and Harp quartets in 2002, and in 2006, a collection of the late quartets received the BBC Music Magazine's Disc of the Year and the Classical Brits Award for Ensemble Album of the Year. Other highlights of the group's performances include series of the complete quartets of Beethoven, Bartók, Brahms, and Schubert in numerous European, American, and Asian cities. The quartet has expanded the conventions of the standard chamber music concert by performing with Robert Pinsky in programs combining poetry and music, and with Muzsikás, the Hungarian folk ensemble, in programs demonstrating the roots of Bartók's and Kodály's quartets in Hungarian folk traditions.

In 1983, the founding members of the quartet accepted the position of Quartet-in-Residence at the University of Colorado, Boulder. Rather than designating them as defectors, the Hungarian authorities grudgingly decided it would be more diplomatic to consider them "cultural ambassadors." Full reconciliation with the Hungarian government came in 2001 when the quartet was given the Order of Merit of the Knight's Cross of the Republic of Hungary. The group has retained its position at the university through its changes in personnel and considers Colorado its home base. It also serves as Quartet-in-Residence at the Aspen Music Festival and as Associate Artists of London's South Bank Center.

The quartet records mainly for Hyperion, and along with its Decca releases, it has also made recordings for Hungaroton and London. In 2019, the Takács Quartet was joined by Marc-André Hamelin for a Hyperion release of Ernst von Dohnányi's piano quintets and second string quartet. ~ Stephen Eddins, Rovi