The guitar came second. Hekselman started on classical piano at six, and didn't pick up a guitar until he was nine. Between twelve and fourteen he was already performing regularly on a weekly Israeli children's television program, which is an unusual kind of stage education for a jazz musician to have logged before puberty. At fifteen he entered the Thelma Yellin School of Arts and graduated with excellence from its jazz department at eighteen.

In 2004 he moved to New York on an America-Israel Cultural Foundation scholarship to study at The New School for Jazz and Contemporary Music. The recognition came fast: in July 2005, still a student, he won the Gibson-Montreux Jazz Festival Guitar Competition in Switzerland. The year after, he released his debut album as a leader, Splitlife (2006, Smalls Records), with bassist Joe Martin and drummer Ari Hoenig — a working relationship with Martin that would carry through several later records.

What followed is one of the more consistent leader discographies in contemporary jazz guitar: Words Unspoken (2008), Hearts Wide Open (2011), This Just In (2013), and Homes (2015) built a quartet sound anchored by Joe Martin on bass and Marcus Gilmore on drums, with saxophonist Mark Turner a recurring voice starting on This Just In. Then the sound opened up. Ask for Chaos (2018) and Further Chaos (2019) brought in Aaron Parks on synths and Rhodes and doubled up the rhythm section with Kush Abadey and Jonathan Pinson, pushing Hekselman's guitar into more electric, groove-driven territory. Zuperoctave: Eyes of the World (2019) and Trio Grande (2020) kept experimenting with format; Far Star (2022) went further still, with Hekselman playing keyboards, bass, whistle, tambourine, body percussion, and voice alongside guitar, largely written during the pandemic.

2024 brought a milestone every serious jazz musician recognizes: a live album recorded at the Village Vanguard, the room with more jazz history packed into a single basement than almost anywhere else in the world. Downhill From Here followed in early 2025, a trio record with bassist Larry Grenadier and drummer Marcus Gilmore that strips the sound back down — probably the simplest record in his catalog since Splitlife — and picked up widely reported 4.5-star reviews from DownBeat.

Along the way he's shared stages and studios with Anat Cohen, Chris Potter, Esperanza Spalding (he appears on her 2012 album Radio Music Society), Mark Turner, Dayna Stephens, Aaron Parks, Jeff Ballard, John Scofield, Ari Hoenig, and Joey Alexander. DownBeat named him its Rising Star guitarist in both 2017 and 2022. In 2018, Pat Metheny personally invited him to play at Metheny's NEA Jazz Master tribute concert at the Kennedy Center, alongside a small group of guitarists Metheny selected himself — about as direct an endorsement as a working jazz guitarist can receive from one of the instrument's defining figures.

Hekselman's playing sits at the more contemporary, groove-conscious end of modern jazz guitar: lyrical and harmonically sophisticated in the quartet records with Joe Martin and Marcus Gilmore, and considerably more electric and textural once synths, doubled drummers, and studio production enter the picture on Ask for Chaos and Further Chaos. The piano-before-guitar background shows up in how compositionally he thinks about the instrument — closer to a pianist's sense of harmony than a pure technician's approach to the fretboard. Far Star, largely self-performed across guitar, keys, bass, and voice, is the clearest evidence of a restless, format-agnostic sensibility; Downhill From Here, by contrast, is a deliberate return to unadorned trio jazz, suggesting a musician who treats "sound" as a choice to be made fresh on each record rather than a signature to be repeated.