Although he did not copy Charlie Parker, Woods was known as the New Bird, a nickname also given to other alto saxophone players such as Sonny Stitt and Cannonball Adderley.

Woods earned the top alto sax player award almost 30 times in DownBeat magazine's annual readers' poll.

[7] Woods, along with Rick Chamberlain and Ed Joubert, founded the organization Celebration of the Arts (COTA) in 1978 late one night in the bar at the Deer Head Inn in Delaware Water Gap.

[4] On September 4, 2015, he performed a tribute to Charlie Parker with Strings at the Manchester Craftsmen's Guild and announced at the end of the show that he would be retiring.

[2] Compilation With Manny Albam With Gary Burton With Dizzy Gillespie With Friedrich Gulda With Quincy Jones With Michel Legrand With Bryan Lynch With Herbie Mann With the Modern Jazz Quartet With Thelonious Monk With Oliver Nelson With Lalo Schifrin With Jimmy Smith With Clark Terry With George Wallington With others