Yonatan "Yoni" Kretzmer was born in Jerusalem in 1982 and picked up the saxophone at fourteen. His first teacher was David Perkins, whom he has described as a larger-than-life figure and a lasting influence; he went on to study in Israel with Erez Barnoi and with the American-born composer and saxophonist Stephen Horenstein. He then moved to Paris to attend the American School of Modern Music, where he worked with Peter Giron and the tenor saxophonist Rick Margitza and took further lessons from Matthieu Donarier while playing the city's clubs.

Back in Israel he became part of the small, tightly connected Tel Aviv improvised-music community of the mid-2000s. His first documented recording is Afternoon High, cut at Bardo Studios in Tel Aviv on July 30 and 31, 2006 by the collective Rats Quartet, with guitarist Ido Bukelman, bassist Daniel Spier and drummer Daniel Feingold; the four shared the writing, four of the nine pieces credited to the group jointly. Over the same years he led two other groups, the free-folk quintet Far From Home (built around two acoustic guitars) and Zork, worked as a sideman for Albert Beger and the clarinettist and painter Harold Rubin, and played alongside Assif Tsahar, pianist Daniel Sarid, Evan Parker, Slava Ganelin, Vladimir Volkov and cellist Yuval Mesner. He also performed at and helped curate the October Jazz Fest, the Red Sea Jazz Festival and the Tel Aviv Jazz Festival.

The group that made his name was New Dilemma, a chamber-and-free-jazz quintet that premiered at the Khan Theater in Jerusalem and put out a self-titled debut on Earsay in 2009 with violist Daniel Tanchelson, cellist Neta Cohen Shani, double bassist Ehud Ettun and Feingold on drums. Haaretz placed it among the year's best five records. Two more dates from the same period sit either side of it: he plays tenor on "Yo Yo Yo" and contributes liner notes to the German drummer Günter Baby Sommer's Live In Jerusalem (Kadima Collective, 2009), and One Afternoon (Kadima Collective KCR 21, 2010) is a trio with Nori Jacoby and Haggai Fershtman.

Kretzmer moved to New York City in 2010 and studied with Ellery Eskelin after arriving. The first record of the New York years had in fact been taped just before the move: Nevertheless, cut at Park West Studios in Brooklyn on November 5, 2009 with Jason Ajemian on bass and Mike Pride on drums, came out on Hopscotch Records in 2010. The following August he co-founded a label. OutNow Recordings launched on August 23, 2011 with a party at the Tel Aviv club Levontin 7 that drew more than 150 people, run jointly by Kretzmer, Ido Bukelman and guitarist Yair Yona and operating across Tel Aviv, Brooklyn and Jerusalem. Its stated aim was to sidestep the classic free-jazz sound rather than reproduce it. The first catalogue number went to Bukelman's Cracked Song; the second, ONR 002, was Kretzmer's own Overlook, a 2011 quartet with bass clarinettist Nitai Levi, bassist Shai Ran and drummer Haim Peskoff. Kretzmer has since done far more than sign records for the label: he designs sleeves, produces, mixes and masters for it, and his name appears in one of those roles on titles by Ehran Elisha, Harold Rubin, Shay Hazan, Hans Tammen, Josh Sinton and others.

Brooklyn gave him a run of working bands rather than one-off sessions. The 2Bass Quartet, with Sean Conly and Reuben Radding on two double basses and Mike Pride on drums, made three records over six years: Weight (2013), the double-disc Book II (recorded at Systems Two on June 9, 2014) and MIS-TAKE (2019). The composition-led 66 Boxes, with cellist Daniel Levin, guitarist Eyal Maoz and drummer Andrew Drury, produced Graceless, taped at The Bunker Studio in Brooklyn and issued in 2013. A trio with bassist Pascal Niggenkemper and drummer Weasel Walter made ProtestMusic in 2014, and Drury returned as a duo partner on Oranges in 2015. Five, recorded at Tedesco Studios on July 22, 2015, put Kretzmer's charts in front of a quintet of Thomas Heberer on cornet, Steve Swell on trombone, Max Johnson on bass and Chad Taylor on drums. Until Your Throat Is Dry, four collective pieces with Ajemian and drummer Kevin Shea, followed within days of it in May 2016.

The later catalogue keeps widening the instrumentation. Esoteric Duos (2016), shared with the Jerusalem bassist Jean-Claude Jones, gives each man his own disc; Kretzmer's is eleven duos with four different bassists. Big (recorded February 28, 2016) is a piano-less trio with Heberer and the Swiss bassist Christian Weber. Seaweed, an afternoon of free improvising with Torbjörn Zetterberg and Andrew Drury at Soup & Sound in Brooklyn, appeared on Different Track Recordings on November 13, 2018. That same year New Dilemma returned in an American form on the double album Months, Weeks and Days, with Josh Sinton on bass clarinet, Frantz Loriot on viola, Christopher Hoffman on cello, Niggenkemper on bass and Flin van Hemmen on drums, its cover carrying photography by Cy Twombly. Bring, taped at Big Orange Sheep in Brooklyn on May 14, 2018 with Daniel Sarid on piano and Michael Evans on drums, closed out the decade in 2019. Kretzmer lives in Brooklyn.

Kretzmer plays with a scorching, serrated tone and a vibrato that Glenn Astarita heard as an improvisational slugfest, and his writing pulls in two directions at once: toward the forward-leaning saxophone lineage of Tim Berne and Ellery Eskelin, and toward the textures of contemporary chamber music, which is what the strings in both versions of New Dilemma are for. He names Albert Ayler, Evan Parker, Peter Brötzmann, Mats Gustafsson, Eskelin, Berne, Cecil Taylor, Archie Shepp, Coleman Hawkins and David S. Ware as his influences, and says a good saxophone sound is one that resonates until and beyond absurdity. Reviewing Five for All About Jazz, John Sharpe called the arrangements classic small-group free jazz played by what came across as a little big band, and compared the session to the Black Saint label in its heyday. Sharpe traced the 2Bass Quartet's twin-bass idea back to Ornette Coleman's Free Jazz and John Coltrane's Africa/Brass, where doubling the bass freed the rhythm section from timekeeping without giving up momentum. Kretzmer distinguishes between his own bands on exactly this axis: he has described the 2Bass Quartet's charts as so vague that a set is close to fully improvised, while 66 Boxes works from pieces with clear chapters and movements.