Peter Eötvös arrived in the Music Academy in 1958 as a child prodigy. It was proposed by Kodály that this boy of exceptional talent, who was educated in Miskolc under the wings of Pál Kardos, and who had been noticed also by György Ligeti two years earlier, should be given a special opportunity to develop his gifts. His first teacher at the Academy was János Viski, with whom Eötvös had a very close, almost parent-child relationship. Besides the strictly conservative educational regime, an important part was played in this by their informal discussions outside the classroom. After Viski's sudden death in 1961, Ferenc Szabó took over the young man, who by then was very active outside the Music Academy as well. Between 1962 and 1964 he was music director at the Vígszinház (Gaiety Theatre), composing dozens of compositions for theatrical and film productions (including the music for István Szabó's film, Álmodozások kora – Age of illusions). Some of these pieces he conducted himself. This theatrical experience had a decisive influence on the rest of his career from several aspects: he recognised the dramatic possibilities inherent in music and got used to adjusting to the given performing conditions, to the fact that a composition is not completed when it is scored, but the performance phase is also a part of it.
He received his diploma in 1965, and in 1966 – with Szabó's support – won a Deutscher Akademischer Austauschdienst (DAAD) scholarship, which enabled him to continue his studies in Cologne. Though the gradual relaxation in the atmosphere of 1960's Hungary made it possible for Eötvös to orientate himself in a relatively wide sphere regarding the various tendencies in contemporary Western European composition, nonetheless, in Germany he received fundamentally new impulses. He studied composition with Bernd Alois Zimmermann, and also received a conductor's diploma. Eötvös came into contact with Karlheiz Stockhausen first as a music score copier, then, from 1968 he became a member of the Stockhausen ensemble as a keyboard player. That is how he got to the Osaka World Fair in 1969, where meeting the thought and lifestyle of the Far East meant an influence for him that accompanied the rest of his life.
Between 1971 and 1979 he worked in the electronic music studio of Westdeutscher Rundfunk, and also acquired as much conducting experience as he could. In 1979 Pierre Boulez invited him to become the musical head of the newly formed Ensemble InterContemporaine; since 1983 he has been working with the Ensemble Modern; between 1985 and 1988 he was principal guest conductor of the BBC Symphony Orchestra, and in 1992-95 of the Budapest Festival Orchestra. He premiered a whole host of contemporary compositions, many of which were recorded on disc as well. The basis of his conducting is the extremely precise analysis of the compositions, and directing the didactic process of the rehearsals in a strictly controlled manner, adapting to the abilities of the musicians. At the same time, this intellectual approach in no way diminishes the captivating, passionate effect of his concerts.
He has not lost touch with Hungary either. From 1970 he participated in the activities of the New Music Studio. Thus, for example, the joint composition written in 1975 with Zoltán Jeney, Zoltán Kocsis, László Sáry and László Vidovszky, Hommage a Kurtág, gave rise later to one of his most important works, Windsequenzen. His 1968 montage, Tale, was composed in the Cologne studio, but used Hungarian folk poetry.
From the mid-1980's his composing activities came more and more to the fore. He was commissioned by various ensembles and radio stations, his new compositions were premiered at festivals, his scores were published by Ricordi and Schott, and several recording companies made discs of them. In his orchestral works (Psychokosmos, 1993; Atlantis, 1995; zeroPoints, 1999) he endeavours simultaneously to use the ensemble to give a spatial effect and to contrast the complex sound blocks and the chamber music-like effects. In his orchestral music, thus in the Chinese opera (1986) composed for a chamber ensemble, in the quartet, Korrespondenz (1992), following the gestures perceived in Mozart's letters, or in the Psalm (1993), composed for percussion instruments in memory of Frank Zappa, he is concerned with achieving a theatre-like effect. His opera, the Three Sisters, based on Chekhov, was premiered in Lyon in the spring of 1993 and won a huge success. It has been performed in several opera houses since, among them in Budapest in April 2000. The opera examines in a dreamlike floating musical ambience the emotional choices leading nowhere, the atomised, illusory hopes of man at the end of the century.
Between 1985 and 1996 Eötvös led a course for young conductors interested in contemporary music at the Szombathely Bartók Seminarium. He established, with the same goal, the International Eötvös Institute in 1993. He became professor of the Karlsruhe College in 1992 and of the Cologne College in 1998. In both places he leads newly established departments for the study of conducting contemporary music. In 1994 he settled in Hilversum, directing the Radio's Chamber Orchestra. He received the title, Chevalier de d'ordre des Arts et Lettres in 1987, and in 1997 the Béla Bartók-Ditta Pásztory Prize.