[1] Mass named the club after Samuel Alexander Mudd, the physician who treated John Wilkes Booth in the aftermath of Abraham Lincoln's assassination.

On the dance floor, DJs David Azarch, Anita Sarko and Johnny Dynell played a unique mixture of punk rock, funk music and curiosities.

[6] Six months after it opened, the Mudd Club was mentioned in People: "New York's fly-by-night crowd of punks, posers and the ultra-hip has discovered new turf on which to flaunt its manic chic.

People associated with frequenting the venue included musicians Lou Reed, Johnny Thunders, David Byrne, Debbie Harry, Arto Lindsay, John Lurie, Nico, Lydia Lunch, X, the Cramps, the B-52's, the Bongos and Judas Priest[10] artist Jean-Michel Basquiat and his then-girlfriend Madonna;[11][12] Colab members; performers Klaus Nomi and John Sex; designers Betsey Johnson, Maripol and Marisol Deluna; underground filmmakers Amos Poe, Eric Mitchell, Charlie Ahearn, Vincent Gallo, Jamie Nares, Jim Jarmusch, Vivienne Dick, Scott B and Beth B, Kathy Acker, and Glenn O'Brien; supermodel Gia Carangi; [13] and makeup artist Sandy Linter.

[18][19] The club has been mentioned in various songs such as "Life During Wartime" (1979) by Talking Heads, "The Return of Jackie and Judy" (1980) by the Ramones, "New York / N.Y." (1983) by Nina Hagen, and "Off the Shelf"(1983) by Elliott Murphy.

In 2022, Judas Priest issued the CD Live at the Mudd Club ’79 as part of their box set, 50 Heavy Metal Years Of Music.