For a long time, Rush didn’t get much respect. The Canadian progressive rock trio built up quite a fan base in the 1970s and ’80s with intricate, layered music, complex concept albums like 2112 and Hemispheres and radio-friendly hits like “Fly By Night,” “Working Man,” “Limelight,” “Freewill” and “Tom Sawyer.” But critics at the time were less enthusiastic, giving the band harsher reviews than many of their fellow top-selling rockers. Unlike a lot of those bands, though, Rush has persisted and thrived for decades now, influencing musicians who grew up listening to their albums, and in recent years the band has finally gotten its due.

In 2012, the band was inducted into the Rock and Roll Hall of Fame after nearly 15 years of eligibility, and Rolling Stone put the band on its cover for the first time last month, completing a turnaround in respect years in the making. The current R40 tour stops in Vegas this week, and celebrates the 40th anniversary of the classic lineup, and band members have said it may be their last full-scale tour. If that’s the case, they’re going out having achieved the acclaim that fans have known they deserved since the beginning.

MGM Grand, 8 p.m. July 25, $59-$179 plus tax and fee. 800.745.3000 Ticketmaster