Murphy was born in Sunflower, Mississippi, and was educated in Memphis, Tennessee, where his father worked at the Peabody Hotel.

In 1948, Murphy moved to Chicago, where he joined the Howlin' Wolf Band, which at the time featured Little Junior Parker.

[5] Murphy recorded two albums and many singles with Chuck Berry and was also featured in works by Koko Taylor, Sonny Boy Williamson II,[4] Buddy Guy, Etta James,[4] and Otis Rush.

[7] He gave a memorable performance in 1963 on the American Folk Blues Festival tour of Europe with his "Matt's Guitar Boogie".

Dan Aykroyd and John Belushi attended one of their performances and subsequently asked Murphy to join the touring band of The Blues Brothers.

The couple later hosted a public reception at Fort Lauderdale, Florida, at which the CD Last Call was released.

[13] The title recording, The Blues Don't Bother Me, was licensed by Universal Records as the second track on the Blues Brothers 2000 Original Motion Picture Soundtrack which earned the RIAA Certified Gold Award of 500,000 units sold on March 16, 1998.

[19] It was a live album featuring many popular blues songs and an instrumental guitar jam.