There are few modern rock craftsmen comparable to Thom Yorke, and few bands whose rockist flag waves more consistently than that of Radiohead. The Oxfordshire schoolmates drew from beloved groups, many of which foreshadowed their own cult appeal—the Pixies, with whom they shared early producers, and the Talking Heads, whose song “Radio Head” gave them a name. In 1991, Radiohead signed to EMI, and the following year delivered a début album bearing a hit that was impossible to ignore. “Creep” became the stuff of alt-radio legend, warmly suicidal and cynically tuned into early-nineties vogue, at once brutal and pitiable. But, alongside tabloid-tantalizing rock stars and engulfing musical movements like hip-hop, it was easy for pop middlemen to ignore the band. Radiohead never chased the crossover success that eventually found it—subverting your surroundings is easier from just left of center.

With each innovative new sound and paradigm shift, Radiohead has rejected the industry tropes that prescribe what a band should do and play. Its devotees, drawn to the group by virtue of its opacity, carve whole identities out of the band’s transgressions. If you’ve ever sparred with a Radiohead fan, you know that “OK Computer” ’s wobbly first steps toward avant-electronica presaged a generation of gear-headed punks, and that “Kid A” ’s abandonment of guitar cliché gives it an unmatched stature in the indie alternative canon—the single “The National Anthem” (2000) manages to make baritone saxophone sound like record scratches. The band has remained dedicated to experimenting with methods of distribution, from decades-ahead streaming services to surprise album releases—benchmarks for which they only occasionally receive credit.

All this may be why, after the May release of “A Moon Shaped Pool,” Radiohead’s ninth studio album, Yorke said he was surprised to find out that people still cared. What insurrections were left? “I cherish the band,” he said recently. “But I don’t expect anyone else to.” Yorke unintentionally echoes the default mode of a Radiohead fan—both brutal and pitiable. For the group’s latest album campaign, it deleted its Web site and all the posts on its social-media accounts, clearing the walls for speculating bystanders to project onto. For two nights at Madison Square Garden, on July 26 and 27, Headheads can live out their love for a group that rarely asks for it, but has patently earned it. ♦