[1] According to Grove Music Online, with a style that draws on "Bartók, Webern and, to a lesser extent, Stravinsky, his work is characterized by compression in scale and forces, and by a particular immediacy of expression".

There, he began his studies at the Franz Liszt Academy of Music, where he met his wife, Márta Kinsker, as well as composer György Ligeti, who became a close friend.

"[7] Kurtág received therapy from art psychologist Marianne Stein, who encouraged him to work from the simplest musical elements, an encounter that revivified him and strongly stimulated his artistic development.

The string quartet he composed in 1959 after his return to Budapest marks this crucial turning point; he refers to this piece as his Opus 1.

[11] Kurtág's first international opportunity came in 1968 when his largest work to date, The Sayings of Peter Bornemisza, was performed by Erika Sziklay and Lóránt Szűcs at the Darmstadt Summer Courses for New Music.

[6] He then lived in the Netherlands (1996–98), again in Berlin (1998–99) and upon invitation by Ensemble InterContemporain, Cité de la Musique, and Festival d'Automne, in Paris (1999–2001).

Kurtág's only opera, Fin de partie, based on Samuel Beckett's Endgame, was premiered at La Scala on 15 November 2018,[13] eight years after the original commission.

His composition, … quasi una fantasia… for piano and ensemble, premiered in 1988, is the first piece in which he explores the idea of music that spatially embraces the audience.

The couple played an always-renewing selection of pieces for two- and four-hand piano from Kurtág's ten-volume collection Játékok as well as transcriptions.

In 2024 Kurtág received the Wolf Prize, an international award granted in Israel, "for his contribution to the world's cultural heritage, which is fundamentally inspirational and human".

Kurtág received the 2014 BBVA Foundation Frontiers of Knowledge Award in the category of Contemporary Music for, in the view of the jury, its "rare expressive intensity".

"The novel dimension of his music", the citation continues, "lies not in the material he uses but in its spirit, the authenticity of its language, and the way it crosses borders between spontaneity and reflection, between formalism and expression.