The band was formed after the Whipped Cream & Other Delights album was released, when live shows made a “real” band necessary. This group disbanded in 1969.

The band members were:
Herb Alpert - Trumpet, vocals
Tonni Kalash - Trumpet
Bob Edmondson - Trombone
John Pisano - Guitar
Nick Ceroli - Drums
Lou Pagani - Piano
Pat Senatore - Bass

In 1974, Herb recorded a new album, You Smile-The Song Begins and formed a new band to tour and promote the album. The second band was known as Herb Alpert & the T.J.B. A third incarnation of the group came together to tour after Herb released the Bullish album in 1984.

It is interesting to note that studio musicians probably played on most (if not all) of the albums, since it seems not all of the band members played on the recordings, even after the bands were formed. There are various sources (including the liner notes of the new TJB CD releases) stating that Herb used session musicians to get the exact sound he wanted.