As manifested in music for his quintet (with Eric Person on sax, Greg Glassman on trumpet, Kenny Davis on bass, and Pete O'Brien on drums) and trio (with Ira Coleman on bass and Pete O'Brien on drums), Esposito's compositions are couched in an expansion of bebop harmony, often using rhythmic schemes of complex and subtle metric modulation.

Born in Brooklyn, Esposito was raised in the Hudson Valley in a family that included policemen but also artists and musicians.

Majoring in musical composition, he drew influences from visiting composers who came through, including John Cage, Robert Ashley, Frederic Rzewski, and Elliott Carter.

In 1980 Esposito moved to New York City, where he worked with saxophonist Arthur Rhames, a neglected, almost forgotten figure who died of AIDS-related illness at 32 (1989), and who some nevertheless feel was the successor to John Coltrane's mantle as the greatest creative performer on that instrument.

Notables he's performed with are Thurman Barker, Nick Brignola, Roy Campbell, Santi Debriano, Carter Jefferson, John Lindberg, Erica Lindsay, Joe Lovano, J. R. Monterose, David "Fathead" Newman, and Roswell Rudd.