Like The Fall, The Cure or the small handful of other bands that clocked a quarter-century without becoming a nostalgia act, The Church have compiled a body of work so huge and have reinvented themselves so many times that newcomers may find their discography too daunting to even think about beginning to explore. The timid and uninitiated, then, may find it best to just pick up a best of or a singles collection and enjoy. For the more picky, adventurous listeners, though, here’s a longer (yet still shamefully abridged) guide to some of the brightest moments in this Australian group’s massive catalogue.

Of Skins and Heart, their 1981 debut, is filled with so many warm, jangly guitar-pop songs that it plays like a singles collection in and of itself. Should-have-been hits like “For a Moment We’re Strangers” and “The Unguarded Moment” presaged the modern rock that would dominate college radio by the end of the decade.

After a couple of albums that toyed with their debuts simple template, to varying degrees of success, The Church went in an entirely different direction for their 1986 second wind, Heyday. Here the sound was rawer, heavier and more guitar-based—The Smith’s The Queen Is Dead is a fairly close comparison—and the songs emphasized longer, razor-sharp solos.

The band soon peaked commercially with 1988’s Starfish, the confident, hooky disc that spawned their biggest hit, “Under the Milky Way,” a gorgeous ballad that climaxes in an odd burst of E-bow guitar, distorted to the point of sounding like bagpipes (the song later became a stand-out on the Donnie Darko soundtrack). The disc’s other single, “Reptile,” was a menacing post-punk jam built around an impossibly sturdy guitar hook that rings in the listener’s head for hours after the track ends.

The public soon lost interest in the band. Eclectic as it was, The Church’s ’90s output was more or less interchangeable. As the alternative-radio revolution passed the band by, they continued toying with long, guitar-heavy, moody-rock songs, gothic themes, psychedelic ambiance and unlikely pop, mostly to commercial indifference.

Riding a renewed wave of interest in 2003 as Donnie Darko became a cult hit and a new generation realized what a stunning song “Milky Way” is, the band released a well-timed non-comeback comeback album, Forget Yourself. There’s nothing new here, except this time around the songs were stronger than usual, more tense and more epic. Its muscular, opening shot, “Sealine,” sounds ripped straight from 1989—if Midnight Oil and Depeche Mode hosted a séance it might have resembled this.

The Church followed up with another satisfying disc, 2005’s El Momento Descuidado, a heavenly acoustic disc reprising many of their best songs. Yeah, it sounds lame on paper—middle aged rockers with bad hair record their non-hits unplugged—but the disc’s somber, haunted aesthetic really works. With a few minimal splashes of piano, muted percussion, vibes and mandolin, the band created an ambiance akin to the hushed, indie-folk albums that were gaining prominence at the time. Of course, the sonic similarities weren’t intentional: By this point in their career, the band has all but given up on trying to sound hip (they certainly don’t look the part anymore, either: recent press photos depict a band you’d see playing a state fair, not Coachella or P4K.) The band will continue to age and most likely continue to fall out of vogue, but as El Momento Descuidado proves, their songs are timeless.

The Church’s guitarist, Marty Willson-Piper, plays a solo show at Shank Hall on Wednesday, May 14.