This page contains information regarding new Star Trek material, and thus may contain spoilers.
(covers information from several alternate timelines)
Rock and roll was a genre of music from Earth, distinguished by a contempt for authority and the status quo, that was first recognized in the 1950s. Tom Paris said that rock and roll "was one of the 20th century's greatest inventions." (VOY: "Virtuoso")
Elvis Presley and John Lennon of The Beatles were popular rock and roll musicians during the mid-to-late 20th century. (DS9: "The Siege of AR-558"; (DIS: "Context Is for Kings") The Jimi Hendrix Experience and Berman's Rainbow Dreamers were psychedelic rock and roll groups during the 1960s hippie-era. When Kira Nerys and Miles O'Brien beamed into the year 1967, they experienced a brief snippet of the classic "Hey Joe", performed by Hendrix's band. (DS9: "Past Tense, Part II")
Punk rock was a subgenre of rock and roll, originating from the punk counterculture of the 1970s. The punk-rock song "I Hate You" by the obscure band Edge of Etiquette was listened to by a punk in 1986. The punk counterculture was still alive a decade later, in 1996. (Star Trek IV: The Voyage Home; VOY: "Future's End")
Even the inventor of warp drive, Zefram Cochrane, liked classic rock and roll music, such as artists Steppenwolf and Roy Orbison, and their works "Magic Carpet Ride" and "Ooby Dooby". In 2378, Neelix played rock and roll music on a jukebox in the USS Voyager's mess hall, celebrating the anniversary of Cochrane's legendary flight. (Star Trek: First Contact, VOY: "Homestead")
In 2376, Ensign Paris told Abarca that there were many different types of music, including rock 'n' roll. Abarca asked if The Doctor performed rock 'n' roll, to which Commander Chakotay replied that The Doctor was more of an opera man. (VOY: "Virtuoso")
In the alternate reality, James T. Kirk listened to "Sabotage" by the Beastie Boys while joyriding in his uncle's Corvette. (Star Trek) 23rd century society deemed some American music of the 20th century as "classical music", as indicated by Spock and Leonard McCoy's comments on the Beastie Boys song "Sabotage". (Star Trek Beyond)