- Born in a family of musicians, his father Hendrik, his uncle and one of his brothers are also composers.
- In 1969, Andriessen co-founded Studio voor Elektro-Instrumentale Muziek STEIM in Amsterdam.
- Andriessen originally studied with his father and Kees van Baaren at the Royal Conservatory of The Hague, graduating in 1961 with a first prize, before embarking upon two years of study with Italian composer Luciano Berio in Milan and Berlin.
- His early works show experimentation with various contemporary trends: post-war serialism (Series, 1958), pastiche (Anachronie I, 1966-67), and tape (Il Duce, 1973).
- He was married in 2012 a second time to violinist Monica Germino, for whom he wrote several works. In December 2020, she announced that the composer was suffering from dementia.
- His opera La Commedia, based on Dante's Divine Comedy, won the 2011 Grawemeyer Award for Music Composition and was selected in 2019 by critics at The Guardian as one of the most outstanding compositions of the 21st century.
- From the early 1970s on he refused to write for conventional symphony orchestras and instead opted to write for his own idiosyncratic instrumental combinations, which often retain some traditional orchestral instruments alongside electric guitars, electric basses, and congas.
- Although his music was initially dominated by neoclassicism and serialism, his style gradually shifted to a synthesis of American minimalism, jazz and the manner of Stravinsky.
- Andriessen was married to guitarist Jeanette Yanikian (1935-2008). They were a couple for over 40 years, and were married in 1996.
- Andiessen repeatedly used his music for political confessions and messages, but he also referred to painting and philosophy.
- He was not only a Dutch composer, but also pianist and academic teacher.
- His range of inspiration was wide, from the music of Charles Ives in Anachronie I, the art of Mondriaan in De Stijl, and medieval poetic visions in Hadewijch, to writings on shipbuilding and atomic theory in De Materie Part I.
- Yale University invited him in 1987 to lecture on theory and composition,and he was also guest lecturer at New York State University, Buffalo (1989) and Princeton (1996).
- His siblings are composers Jurriaan Andriessen and Caecilia Andriessen (1931-2019), and he is the nephew of Willem Andriessen (1887-1964).
- In opposition to the classical orchestra, a structure seen as "hierarchical", he also helped founding the instrumental groups Orkest de Volharding and Hoketus, both of which performed compositions of the same names, formed by classical, jazz and pop musicians.
- From 1961 to 65, Andriessen wrote for the daily De Volkskrant, and for De Gids magazine from 1966 to 1969.
- Andriessen taught at the Royal Conservatory of The Hague from 1974 to 2012, influencing notable composers.
- The arts faculty of the University of Leiden appointed him professor in 2004.
- Considered the most influential Dutch composer of his generation, he was a central proponent of The Hague school of composition.
- His reaction to what he perceived as the conservatism of much of the Dutch contemporary music scene quickly moved him to form a radically alternative musical aesthetic of his own.
- By the 21st century he was widely regarded as Europe's most important minimalist composer.
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