Ralph Alessi (born March 5, 1963) is an American jazz trumpeter, composer, and ECM recording artist. Alessi is known as a virtuosic performer whose critically-acclaimed projects include his Baida Quartet, with Jason Moran, Drew Gress, and Nasheet Waits, and This Against That, his quintet with Andy Milne, Gress, Mark Ferber, and Ravi Coltrane. Alessi has also recorded and performed with artists including Steve Coleman, Uri Caine, Fred Hersch, and Don Byron.

Alessi is known for his work as an educator, and in 2001 he founded the School for Improvisational Music in Brooklyn, New York. He has taught at the Eastman School of Music, NYU, NEC, the University of Nevada, Reno, Siena Jazz University, and University of the Arts Bern.

Alessi was born and raised in the San Francisco Bay Area. His parents met as performers at the Metropolitan Opera: his mother, Maria Leone Alessi, sang in the chorus; his father, Joseph Alessi Sr., was principal trumpet for nearly 15 seasons. His brother, Joseph Alessi, is a trombonist with the New York Philharmonic.

Alessi also began as a classical musician, and performed with the San Francisco Symphony and San Francisco Opera in his teens. He later attended the California Institute of the Arts, studying with Charlie Haden while earning a BFA in jazz trumpet performance and MFA in jazz bass performance. In 1986, he met fellow CalArts student Ravi Coltrane, who became one of his longest-standing collaborators. JazzTimes describes their "musical bond" as "arguably developing into a rapport on par with the highest echelon of trumpet/tenor combinations"; Coltrane once gave an interview with NPR focused entirely on his favorite song, Alessi's "Who Wants Ice Cream".

With David Ake

With Don Byron

With Michael Cain

With Uri Caine