My Chemical Romance may be the perfect new millennial rock band.

Always poised for a significant hit, they instead wound up with a devoted cult following that peaked around the release of 2006's The Black Parade, a gobsmacked concept album on par with Pink Floyd's The Wall or maybe Marilyn Manson's Antichrist Superstar, but MCR were always more in tune with teen angst and were always more fun, as the 2014 hits compilation May Death Never Stop You: The Greatest Hits 2001-2013 proves.

The 19-track compilation contains three demos plus the new song "Fake Your Death," which opens a compilation that otherwise diligently marches forth in chronological order.

The debut, I Brought You My Bullets, You Brought Me Your Love, is dismissed with two songs -- "Honey, This Mirror Isn't Big Enough for the Two of Us" and "Vampires Will Never Hurt You" -- leaving the molten rock of Three Cheers for Sweet Revenge plenty of room, but The Black Parade is the centerpiece of this collection, as it's represented with five songs and its strong follow-up, Danger Days: The True Lives of the Fabulous Killjoys, has four songs.

The key to Black Parade and Danger Days is how MCR embraced theatricality -- the overblown drama inherent to leader Gerard Way's beloved comics -- and they could translate it well to record.

They had records worth hearing in full -- The Black Parade, certainly, plus Three Cheers and Danger Days -- but the great thing about May Death Never Stop You is how it showcases all their brilliant, florid moments so they sound like visionaries without a continent to call home.

Maybe they could've been bigger stars, but they channeled all the sturm and drang of the new millennium into heady goth-punk operas that still sound great when broken down into their individual elements, as this fine compilation proves.