Two progressive metal concept/thematic albums, both of which I brought up in a recent college essay, are Voivod's Dimension Hatröss and Toxik's Think This.
Dimension Hatröss is musically very technical and angular, and lyrically tells a sci-fi story about an entity (who appears on the covers of Voivod's first five albums in different forms) who creates his own dimension with a particle accelerator, only to discover that it's fraught with similar social divisions and conflicts to the world he comes from. Ultimately, he gets into battles with other psychic beings and ends up escaping from the world of his own creation before deeming it a failed experiment and destroying it. Think This is musically more straightforward, but still complex in places. It's less of a "story" type concept album and more a thematic piece. Almost all the songs are themed around various social problems, but with an emphasis on how mass media (in 1989, that would be TV and radio) helps exacerbate these problems. Owing to that, there are a couple songs directly about TV, and nearly every song begins with a sample of a radio or TV broadcast, usually an advertisement but sometimes a speech from a religious leader or politician. Full of Reagan-era countercultural rage; even the album cover is pure 80s.
Going in a completely different direction musically, there's A Crow Looked at Me and its recent sequel Now Only, two incredibly sad folkish albums from Mount Eerie, a project of Phil Everum (formerly of The Microphones). They'll hit you like a ton of bricks. To make it short, Phil's wife died a year after being diagnosed with cancer, and those two albums are themed around his grief over her passing (as well as meditations on death in general), with A Crow Looked at Me being particularly heartwrenching since it was entirely written mere months after her passing.