Aviv Cohen was born and raised in Jerusalem and did not sit down at a drum kit until he was sixteen, a late start for a player who would end up holding one of the two drum chairs on an ECM record. He studied at Rimon School of Jazz and Contemporary Music in Ramat HaSharon, then moved to New York to study further, and has worked as a professional drummer and recording artist since 2003. He is based in Tel Aviv-Yafo. Since the early 2000s his closest musical partner has been guitarist and bassist Yonatan Albalak, a fellow Jerusalem native; the two have shared bandstands in three separate groups across roughly two decades. Cohen records and produces under the alias Sol Monk, sometimes written Solmonk.

His first sustained band was LayerZ, a trio with Albalak on guitar and synth and Gilad Abro on bass, working a seam of post-rock, electronica and improvisation. LayerZ issued LayerZ EP1 on March 22, 2011, Memory Towers in 2013, and Things On Top Of Each Other on June 22, 2015, the last of them bringing in Nitai Hershkovits on keyboards and piano, singer Marina Maximilian Blumin, saxophonist Eyal Talmudi and vocalist KerenDun as guests. The band's own liner note for that record marks the point where its members split off in different directions: Albalak started writing lyrics and singing, Abro went deeper into bass, and Cohen "recorded a solo album (Sol Monk) and got more into beats/electronica."

That solo album was Beats, Not Words, released November 4, 2014 on Time Grove Selections in partnership with the Tel Aviv label Raw Tapes, co-produced with Rejoicer and cut as thirteen short instrumental pieces built from live drums and sampled material. Cohen followed it with Turn Left on September 12, 2015, four beats made in five days in Berlin with Free The Robots and Rejoicer at DJ Werd's Luck Hour Studios, then Make Time on January 4, 2016, a set of home-made beats with guests including Nitai Hershkovits on keys, trumpeter Roei Hermon and bassist Avri Borochov. The Sol Monk project went quiet for nearly a decade before returning as a working trio with guitarist Tamuz Dekel and bassist Dor Samoha: New Moves arrived March 7, 2025, and Sands Don't Sleep on May 15, 2026, the latter produced with Rejoicer, who also plays keys and bass on it.

In late 2015 Cohen, Albalak and the producer and vocalist Shuzin formed Geshem, the Hebrew word for rain. The trio's debut Sungazing came out May 30, 2018 on Ghostown Records (GR001) as a twelve-track LP with sleeve art by Kip of the Haifa graffiti crew Broken Fingaz; the follow-up Nomad Fire landed May 21, 2021 through Raw Tapes, with a string section (Yogev Glusman, Keren Tannenbaum and Yael Shapira) arranged by Albalak on four of its ten tracks. Cohen plays drums, bells and percussion on the record and shares its composing credits.

The band that put him in front of an international jazz audience came in 2019, when trumpeter Avishai Cohen brought him into Big Vicious, a twin-drummer electric quintet completed by Ziv Ravitz on drums and live sampling, Uzi Ramirez on guitar and Albalak on guitar and bass. The group's self-titled album was recorded in August 2019 at Studios La Buissonne in Pernes-les-Fontaines, produced by Manfred Eicher, and issued March 27, 2020 as ECM 2680. The two drummers are used less as a rhythm-section doubling than as a pair of separate textures, one keeping the floor and the other stretching it, and Cohen's half of that arrangement leans on his beat-making instincts as much as his kit playing.

Away from his own bands, Cohen has been a first-call session drummer on the Israeli scene since the late 2000s. He is the drummer on Daniel Zamir's 2010 album Missing Here, in a band with Omer Avital on bass, Omer Klein on piano and guest appearances by trumpeter Itamar Borochov and trombonist Avi Lebovich, and he held the chair in the Itamar Borochov Quartet for Outset (2014). He has recorded with singer Marina Maximilian, guitarist Tamar Eisenman, and ney player Itzhak Ventura, whose Aligned came out on Riverboat Records in 2022. Within the Raw Tapes orbit he turns up repeatedly on records by Rejoicer, Nitai Hershkovits, Time Grove, Buttering Trio and Maya Dunietz, and since 2020 he has co-led Duo Brothers with guitarist and bassist Yonatan Levy, recording and engineering both of their albums himself at Saloniki Studios in Tel Aviv. He has also toured with Yemen Blues and Eyal Talmudi. He endorses Istanbul Mehmet cymbals and Innovative Percussion sticks.

Cohen works the seam between a jazz drummer and a beat producer, and the two halves feed each other rather than alternating. On the kit he is credited with a heavy, unhurried pocket and a clean, technically exact stroke, and his own label's copy describes his drumming as a mix of tightness, soul and technique. On record he treats the drum part as raw material: Beats, Not Words and Make Time are largely his own playing chopped, sampled and rebuilt, and the same instinct shows up in Big Vicious, where the two-drummer format lets one kit hold a loop-like figure while the other floats above it. His touchstones are audible in the company he keeps rather than in any stated lineage: the Raw Tapes producers around Rejoicer on one side, and the Israeli jazz mainstream of Avishai Cohen, Omer Avital and Itamar Borochov on the other. Where most Israeli drummers of his generation moved toward New York straight-ahead playing, Cohen went the other way, into post-rock, trip-hop and IDM with Geshem and LayerZ, and brought that vocabulary back into a jazz setting when ECM came calling.