Rihm was professor of composition at the Hochschule für Musik Karlsruhe from 1985, with students including Rebecca Saunders and Jörg Widmann.

[4] He was an enthusiastic choir singer, and he often improvised on the organ, creating "sound orgies" in the style of French organists.

[6] At the Hochschule für Musik Karlsruhe, he studied music theory and composition with Eugen Werner Velte [de] while still attending secondary school.

[5] Rihm then enrolled at the Hochschule für Musik Freiburg from 1973 to 1976, studying composition with Klaus Huber[8] and musicology with Hans Heinrich Eggebrecht.

[4] Rihm followed Velte's approach of educating in open dialogue with the individual student, cultivating freedom of thought.

[4] His opera Die Hamletmaschine, composed between 1983 and 1986 based on Heiner Müller's play, Hamletmachine, premiered at the Nationaltheater Mannheim in 1987.

[17] He based the libretto for his opera Oedipus, commissioned by Deutsche Oper Berlin on the Greek tragedy by Sophocles and related texts by Friedrich Nietzsche and Heiner Müller.

[20][21] At Walter Fink's invitation, Rihm was the fifth composer featured in the annual Komponistenporträt of the Rheingau Musik Festival in 1995.

In 2003 Rihm received the Ernst von Siemens Music Prize, as ... one of the most prolific and versatile composers of our time.

With inexhaustible imagination, a vital creative drive and keen self-reflection, he has created an oeuvre rich in facets, which already comprises over four hundred compositions from all musical genres.

Rihm's music manifests his belief in the indestructible existence of the creative individual, who is able to assert his strength and dignity against all external threats.

Matthias Rexroth sang his Kolonos | 2 Fragments by Hölderlin after Sophokles for countertenor and small orchestra in 2008 at the Bad Wildbad Kurhaus, with Antonino Fogliani conducting the Virtuosi Brunensis.

[26][27] In March 2010, the BBC Symphony Orchestra featured Rihm's music in one of their 'total immersion' weekends at the Barbican Centre in London.

[28] On 27 July 2010, his opera Dionysos (on Nietzsche's late cycle of poems Dionysian-Dithyrambs) was premiered at the Salzburg Festival by Ingo Metzmacher with sets designed by Jonathan Meese.

[32] Anne-Sophie Mutter and the New York Philharmonic premiered his violin concerto Lichtes Spiel (Light Games) in Avery Fisher Hall on 18 November 2010.

[1] On 11 January 2017, the Elbphilharmonie in Hamburg was inaugurated with the premiere of Reminiszenz, a song cycle for tenor and large orchestra that he composed on a commission for the occasion.

[1] In the late 1970s and early 1980s, his name was associated with the movement called New Simplicity (Neue Einfachheit), a term popularized by Aribert Reimann.

[42] Nonetheless, Yves Knockaert considered that there were important philosophical and stylistic affinities, especially between Rihm's music and the work of Georg Baselitz.

[21] Rihm grouped particular themes in cycles, like Chiffre, Vers une symphonie-fleuve, Séraphin, and Über die Linie.

[46] Rihm's students included Rebecca Saunders,[1] David Philip Hefti, Márton Illés, and Jörg Widmann.

[14] Saunders said about his teaching that "he fought steadily and consequently against polemic thinking, and he encouraged a decidedly personal aesthetic unique to each of his many students.