Claudio Fasoli was born in Venice on 29 November 1939 and has spent most of his working life in Milan. He plays tenor and soprano saxophone, and also flute. He is a composer first in the way he builds records: on most of his own albums, every piece on the sleeve is his.

The wider audience found him through Perigeo. The band came together in Rome in 1971 with Fasoli on saxophones, Giovanni Tommaso on bass, Franco D'Andrea on keyboards, Bruno Biriaco on drums and Tony Sidney on guitar, and it recorded for RCA Italiana across the decade: Azimut (1972), Genealogia (1974), La valle dei templi (1975), Non è poi così lontano (1976) and Fata Morgana (1977). Perigeo is filed under progressive rock as readily as jazz, and its catalogue has kept circulating, with Sony and RCA issuing an Antologia set in 2014 and the band recording a live reunion in Florence in July 2019.

His own discography begins the year after Perigeo stopped, and it begins in the smallest possible form. Jazz Duo (Dire, 1978) is Fasoli and Franco D'Andrea, saxophone and piano, with liner notes by the critic Arrigo Polillo. He led a trio on Eskimo Fakiro (Carosello, 1977), a quartet with Pat LaBarbera on The Meeting (1979), and his own Jazz Group on Hinterland (1980).

The run that established him internationally came through Soul Note, the Milan label run by Giovanni Bonandrini. Lido (SN 1071, 1983) put Fasoli in front of Kenny Drew on piano, Niels-Henning Ørsted Pedersen on bass and Barry Altschul on drums, with every composition his own. Welcome (SN 1171), recorded on 26 March 1986 and issued the following year, brought in Kenny Wheeler on trumpet and flugelhorn, Jean-François Jenny-Clark on bass and Daniel Humair on drums. Nat Hentoff wrote the English liner notes; Humair painted the cover. On both records the visiting players are reading Fasoli's charts.

He then spent two decades taking the band apart and rebuilding it. Land (1989) kept Wheeler and Jenny-Clark and removed the drums entirely. Bodies (1990) went electric, with Mick Goodrick on guitar and guitar synthesizer, Palle Danielsson on double bass and Tony Oxley on drums and percussion, and drew liner notes from Art Lange and Maurizio Franco. Cities (RAM, 1993) kept Goodrick and replaced the rhythm section with Paolino Dalla Porta and Bill Elgart; Fasoli produced it, mixed it with Giancarlo Barigozzi, wrote its notes and shot its photographs. Mirror (RAM, 1996) reduced the music to three voices, with Jay Clayton singing and running live electronics beside Stefano Battaglia on piano. In November 1996, at Movin' Studio in Saccolongo near Padova, he recorded Icon with Enrico Rava on trumpet and D'Andrea on piano, a trio with no bass and no drums.

Alongside his own groups he worked inside other people's. He was a member of the Giorgio Gaslini Quintet, appearing on Multipli (1988) and Masks (1992), of the Guido Manusardi Quartet on Live Suite (1974), and of the Lydian Sound Orchestra, whose Azurka (Abeat, 2003) is co-billed with him. He recorded with Tiziana Ghiglioni and Emanuele Parrini on Rotella Variations (2003), and he has worked in a trio with Rita Marcotulli and Bobo Stenson. In 2007 he made Infant Eyes, a programme of Wayne Shorter compositions, with Lee Konitz.

The late period is the one that resists the usual shape of a veteran's career. On 8 June 2017, aged 77, Fasoli recorded at System Two Recording Studio in Brooklyn with Matt Mitchell on piano, Matt Brewer on bass and Justin Brown on drums; the album, Selfie, came out on Abeat in 2018. Three years earlier he had made The Brooklyn Option at Artesuono in Cavalicco with Ralph Alessi, Mitchell, Drew Gress and Nasheet Waits, its track titles naming Brooklyn Bridge, Carroll Gardens, Bay Parkway and Gowanus; Abeat reissued it in 2019 under the Claudio Fasoli 5et billing. Since 2021 his working group has been the NeXt 4et, with Simone Massaron on electric guitar and electronics, Tito Mangialajo Rantzer on double bass and Stefano Grasso on drums, which has made Next (2021), Ambush (2023) and Hasard (2024) for the same label. His Samadhi quartet, with Michelangelo Decorato, Piero Leveratto and Marco Zanoli, released A Long Trip 22 on Parco della Musica Records in 2025.

He has taught throughout. Fasoli has been on the saxophone faculty of the Siena International Jazz Clinics since 1978, founded the saxophone courses at Milan's municipal jazz school, and has taught in the Italian national conservatories. From 2003 to 2010 he was artistic director of the Padova Jazz Festival. In the 2018 Top Jazz critics referendum run by Musica Jazz he was voted Musician of the Year, and the same magazine named Next the best Italian jazz CD of 2021. He appears in Leonard Feather and Ira Gitler's Biographical Encyclopedia of Jazz (Oxford).

Discogs catalogues 121 credits under his name, 24 of them credited directly to him as a leader, alongside a further run of records issued under his own ensemble names: the Jazz Trio, the New Quartet, the Jazz Group, the Experience, the Gammatrio, the Emerald Quartet, the Double Quartet, the N.Y. 4et, the Samadhi group and the NeXt 4et.

Fasoli's writing is the constant. From Lido through Bodies he credited every composition to himself, and the shape of each record comes from the instrumentation he chose for it rather than from a repertoire he was working through. His own term for the approach, given on his site, is a "modal complex" method built through trios and quartets.

Two impulses run in parallel across the catalogue. One is subtractive: the drummerless quartet of Land, the voice-piano-saxophone triangle of Mirror, the horn-and-piano trio of Icon, the saxophone-and-bass duo of Duology (2012). The other is electric and textural: Mick Goodrick's guitar synthesizer on Bodies, Jay Clayton's live electronics on Mirror, and Simone Massaron's guitar and effects across the three NeXt 4et records. He tends to move between the two rather than settle in either.

The Perigeo years put him inside Italian jazz-rock at its point of highest visibility, and almost nothing in his later work sounds like it. Nat Hentoff, writing the English liner notes for Welcome in 1987, and the critic quoted on Fasoli's own site both single out the same quality: a narrative clarity, the sense of a player using the horn to say something in sequence rather than to display material.