Roberto Tarenzi was born in Milan, Italy, in 1977. He began classical piano studies at age eight and discovered jazz in his teens, attending Ray Santisi's Berklee-affiliated seminar at Umbria Jazz in 1994 and studying with Franco D'Andrea and Enrico Pieranunzi at Siena Jazz in 1996. He completed his diploma in 1999 at Milan's Civici Corsi di Jazz, where his teachers included Enrico Intra and Roberto Pronzato.

From 1995, at age eighteen, he played piano in the Civici Corsi di Jazz Big Band directed by Enrico Intra, recording four albums with the ensemble. His own biography and multiple independent profiles describe the band backing visiting American and Italian jazz figures including Dave Liebman, Max Roach, Bobby Watson, Bob Brookmeyer, David Murray, Eddie Daniels, Franco Cerri, Enrico Rava and Franco Ambrosetti during this period; none of these appearances carries a matching Discogs release credit under Tarenzi's own name, so they are reported here as consistently documented performance history rather than confirmed studio collaborations.

In 2000, inspired by the music of Ahmad Jamal, Tarenzi founded the CUES Trio with bassist Lucio Terzano and drummer Tony Arco, releasing Introducing Cues T (Black Saint, 2002). The trio went on to record two studio albums with American saxophonist Dave Liebman, Dream of Nite (2007) and Negative Space (2008), both cut from a series of 2005 Italian live dates and issued internationally on EmArcy/Verve.

In September 2006 Tarenzi was selected as one of twelve pianists worldwide to compete in the Thelonious Monk International Piano Competition in Washington, D.C., reaching the final round before a jury chaired by Herbie Hancock. He spent several months living and working in New York City afterward before returning to Italy. In July 2008 he toured Japan with vocalist Alice Ricciardi, the same year he recorded on her Blue Note album Comes Love.

Since 2008 Tarenzi has been based in Rome, where he has released a steady run of albums as a leader - 13 Floors (2007), Dig Deep (2009), Involving Evolving Revolving (2011, featuring Stefano Di Battista and Dario Deidda), Other Digressions (2013, featuring Rosario Giuliani), a live trio album with Dario Deidda and Roberto Pistolesi (2015), Love and Other Simple Matters (2018, with American bassist John Patitucci's Ahmad Jamal Trio colleague James Cammack and drummer Jorge Rossy), and 11 Little Things (2019, again with Dario Deidda and Roberto Pistolesi) - while working widely as a sideman. Notable guest credits include Rosario Giuliani's Images (2013), co-billed with vibraphonist Joe Locke, bassist John Patitucci and drummer Joe LaBarbera, and a piano credit on the soundtrack to Paolo Sorrentino's Oscar-winning film La Grande Bellezza (2013). He teaches jazz piano, including at Rome's Saint Louis College of Music and at Milan's Civica Scuola di Musica Claudio Abbado, and leads improvisation workshops.

Tarenzi's playing moves between two clearly audible poles. One is the Ahmad Jamal-rooted trio writing that produced the CUES Trio and later his own working trios with Dario Deidda and Roberto Pistolesi: economical, groove-conscious, built on space as much as notes. The other, heard most clearly on the two Dave Liebman-led quartet albums Dream of Nite and Negative Space - Discogs tags the former Free Jazz and both Contemporary Jazz - is a looser, more harmonically open language shaped directly by playing alongside an American avant-garde-adjacent improviser on his own terms. His formal teachers span both ends of that range: Franco D'Andrea and Enrico Pieranunzi for harmonic depth, Ray Santisi for a Berklee-style grounding in the standard repertoire. The 2010s leader albums, tagged Post-Bop and Contemporary Jazz on Discogs across the board, sit closer to the compositional, quartet/quintet mainstream of contemporary Italian and European jazz, often built around frequent working partners such as Rosario Giuliani, Stefano Di Battista and Roberto Pistolesi.