Miles Davis was one of the most important musicians of the 20th Century. How important? He’s one of the two or three jazz musicians non-jazz fans have heard of, and may even have heard something by.

Davis reshaped jazz in his own image multiple times. The ideas explored on his 1965-68 quintet albums, for example, cause many to still regard them as the pinnacle of acoustic jazz; his and his bandmates’ melodic, harmonic and rhythmic innovations are still being explored (not to say imitated) by present-day musicians. On the other hand, major portions of his catalog are as controversial today as they were the day of their release. Many jazz fans and jazz critics insist nothing he recorded after 1968 is actually jazz at all (a statement I happen to agree with; I just don’t think of that as a bad thing).

Davis got his start in the 1940s, moving from his native East St. Louis, IL to New York to study at Juilliard, and promptly heading for Harlem to play with Charlie Parker, Thelonious Monk and other already established figures on the bebop scene. He first recorded as a leader in 1946, at the same time that he was a member of Parker’s band, and appearing on numerous recordings that are still regarded as landmarks in jazz history. His trumpet style was completely different than that of his predecessor, Dizzy Gillespie — he avoided rocketing high notes in favor of a more melodic approach that didn’t always mesh perfectly with what Parker and his bandmates were doing, but would ultimately become one of the most influential sounds in jazz.

In the 1950s and 1960s, Davis emerged as one of the most famous jazz players in the world, not just for his music but for his image as well. He was featured in magazines for his personal style, and interviewed by Playboy when that was extremely prestigious. And the music he made — whether with his first quintet, featuring John Coltrane, or his mid-’60s quintet with Wayne Shorter and Herbie Hancock, or with Gil Evans’ orchestra — always stretched boundaries, always challenged his contemporaries to keep up.

His 1959 album Kind Of Blue is a genuine musical landmark; artistically unimpeachable, it’s also one of the most commercially successful jazz records of all time. It’s so important in the genre’s history that this year, the fiercely talented but also somewhat pranksterish group Mostly Other People Do The Killing released Blue, a note-for-note (and sound-for-sound; they attempted to recreate the players’ styles and the vintage sound as well) re-recording of it, to widespread bafflement and outrage from jazz fans, most of whom are apparently unfamiliar with conceptual art.

In 1969, though, everything changed. Influenced by jazz’s diminishing sales and public profile, and his young second wife, Betty Davis, began the process of turning away from acoustic music and toward an entirely new sound. At first, on albums like In A Silent Way and Bitches Brew, it was called “fusion” or “jazz-rock,” but as the ’70s began, and he abandoned jazz clubs for rock festivals and theaters, it got more and more aggressive and funky. 1972’s On The Corner, noisy and chaotic, was a challenge to pretty much anyone who’d ever liked him — of course, it was also one of his most brilliant releases. And between 1973 and 1975, he almost abandoned the recording studio in favor of the stage, fronting a band that blended funk, metal, jazz, African music and sounds never before heard by anyone, assaulting audiences at top volume through amps painted red, black and green.

Between 1976 and 1980, Davis disappeared entirely, burrowing into a giant pile of drugs and groupies in his Manhattan apartment. When he re-emerged, his music was stripped down pop-funk. By 1985’s You’re Under Arrest, he was covering tunes like Michael Jackson’s “Human Nature” and Cyndi Lauper’s “Time After Time” … and making it work, giving them all the emotional weight of the jazz standards he’d recorded in his 1950s acoustic heyday. In the final year of his life, he turned his attention to hip-hop, working on Doo-Bop with producer Easy Mo Bee, who’d later create tracks for Notorious B.I.G., 2Pac, Wu-Tang Clan, and Alicia Keys. Davis died before the album could be completed.

Ranking a catalog the size of Miles Davis’ is an impossible task. There are so many lavish boxed sets, live releases, compilations issued during his hermit period, etc., that in order to make this article at all manageable, major cuts had to be made before it could even be begun. So here’s how this is going to work: I chose studio albums only. But to truly understand Davis’ catalog, there are a bunch of essential live releases, including Live-Evil, In Concert: Live At Philharmonic Hall, Dark Magus, Agharta, Pangaea, and The Bootleg Series Vol. 1: Live In Europe 1967. So consider the 30 albums below a starting point. There’s so much more.

Start the Countdown here.