I don't know how "relevant" these bands are today, but they are the stuff of my youth. I was a little more into AC/DC, Judas Priest, Krokus, UFO, Scorpions, Led Zeppelin and the like, but listened to and saw my share of more pop oriented bands like Styx, Foreigner, Heart, and some of the others mentioned.
The cool thing is that many of them are still around and touring and playing smaller venues with much better sound systems than "back in day". In the last few years I've seen a lot of great shows, mostly at "affordable" prices - Styx, Foreigner, Cheap Trick, Heart, Bad Company, Joe Walsh, Fleetwood Mac, Yes, Brian Wilson, War, Todd Rundgren/Utopia, to name a few. While many of them don't have all their original members, they usually sound great. They've had a lot of time to practice and refine their stage shows!