Saturday Night Live Band

The Saturday Night Live Band (referred to in the closing credits as The Live Band) is the house band of the NBC television program "Saturday Night Live" ("SNL").
Role on "Saturday Night Live".
The band consists of mostly jazz, R&B, and some rock musicians and features a strong horn section. They normally play the opening theme music (after the cold opening), musical pieces in between commercial breaks, and the closing theme music "Closing Theme (Waltz in A)," written by founding member Howard Shore. Often, the band will provide the music to a sketch when necessary.
Band leaders and musical directors.
Musician and future Academy Award winning film composer Howard Shore was the original musical director and bandleader from 1975 until 1980.
Singer and songwriter Kenny Vance (who appeared previously as a musical guest on the May 21, 1977 episode) became the musical director for the show's sixth season (1980-81). Original band member and trombonist Tom Malone took over leadership duties under executive producer Dick Ebersol's tenure from 1981 to 1985. Hall & Oates guitarist G.E. Smith came on board as the new musical director once original producer Lorne Michaels returned and stayed in that position until 1995 when lead saxophonist Lenny Pickett was promoted as bandleader.
Katreese Barnes also served as the music director for a time, around the year 2000. 
Keyboardist Leon Pendarvis (who has been a member of the band since 1980) is also 2nd musical director alongside Pickett.
Other projects.
Mariah Carey utilized the horn section of the Saturday Night Live Band (Lew Delgatto, Lenny Pickett, George Young, Earl Gardner, and Steve Turre) for her performance of "If It's Over" during her 1992 "MTV Unplugged" special.
Tom Malone, Lou Marini, and Alan Rubin were members of the Blues Brothers band fronted by SNL cast members John Belushi and Dan Aykroyd. They were also featured in the Blues Brothers movie, with Malone as a member of fictional lounge act "Murph and the Magic Tones," Rubin as maitre d' of an expensive French restaurant, and Marini as a fry cook at Aretha Franklin's soul food restaurant. Paul Shaffer was also involved in early Blues Brothers performances, but had scheduling conflicts and could not appear in the film.
Members.
Past members.
Founders
1970s additions
1980s additions
1990s additions
2000s additions