Joseph Alessi is among the world's preeminent trombonists, widely active as an orchestral player and as a soloist. He has also played jazz and is an important educator. Alessi spent a year as principal trombonist with the Montreal Symphony Orchestra, and then, in 1985, he earned the same position with the New York Philharmonic. He remained there as of the mid-2020s. In 1986, he joined the faculty at the Juilliard School in New York; he continued to hold that position as well in the mid-2020s. In 1991, Alessi made his recording debut with the holiday album Trombones Under the Tree. In 2023, he released the album Joe's Tango: Concerto for Trombone & Other Works. That year, he gave the U.S. premiere of the Trombone Concerto by jazz pianist and composer Chick Corea.