Whether we’ve sought them out or not, most of us know a few Steve Miller Band songs. Seventies hits like “The Joker” and “Fly Like an Eagle”—and a half dozen others—remain common in ads and soundtracks, omnipresent where kegs are popular, and ubiquitous on classic rock radio. Miller refers to those biggest singles as “chocolate cake.” They’re warm and sweet comfort food, a cookout-ready version of escapist, inescapable pop-rock.

But while the hits are the main source of Miller’s fame, there’s a lot to appreciate before and after dessert. To get a full sense of the Steve Miller Band, it’s good to start with his early influences, like his godfather Les Paul, then move on to early collaborators like Muddy Waters and the Grateful Dead, artists he met in Chicago blues clubs and Haight-Ashbury communes. Then it makes sense to sample his early, out-there psychedelia and his pre–Greatest Hits pop jams. After that we’re on to the chocolate cake, where one can hear, at the sonic edges of the hits, many of those earlier influences. Then, to close, there’s his late-career inner weirdness and the many artists he went on to influence himself. With that in mind, here’s a fifty-song, somewhat chronological playlist:

1948–1961: Mentors and Influences (“Steve Miller Age 5 Talking to His Godfather Les Paul” through “Travelin’ Man”): Miller had a gilded musical childhood; legendary sonic innovator Les Paul was his godfather, and T-Bone Walker taught him how to play guitar behind his back. His Dallas rearing also gave Miller a mix of country, blues, and rock on the radio, and lots of world-class acts to see live.

1960–1967: Pre-Fame Stage Partners (“Baby, What You Want Me to Do” through “C.C. Rider”): In his teens and twenties, Miller grew into a kind of rock music Forrest Gump. He was everywhere at the right time: in London with the Beatles, at festivals with Jimi Hendrix. Most foundational were his stint in the Chicago blues scene, his European tour with the Supremes, and his years in the San Fransisco psych-rock movement.

1968–1972: Early Trips (“The Beauty of Time Is That It’s Snowing (Psychedelic B.B.)” through “Journey From Eden”): You might not know it from “Abracadabra,” but Mr. Steve was a real hippie. San Francisco cops harassed him for his long hair, the Fillmore Auditorium regularly featured his psychedelic blues rock, and Jann Wenner himself wrote that the first Steve Miller Band album “ranks with Sgt. Pepper in terms of taste.”

1969–1972: Proto-hits (“Living in the U.S.A.” through “High on You Mama”): Even before his mid-seventies FM reign, Miller was crafting hook-filled, pop-leaning songs and collaborating with Paul McCartney. These rank among my favorite Steve Miller Band tracks.

1973–1982: Hits (“Take the Money and Run” through “Abracadabra”): For many people, Steve Miller is a Greatest Hits artist. And although there’s more to his discography than that, there’s no denying these songs’ durability and craft.

1981–2015: Later Trips (“Macho City” through “Come On In My Kitchen”): In later years, less burdened by the spotlight, Mr. Steve got idiosyncratic again. He recorded sixteen-minute disco freak-outs, synthesizer love ballads, and a lot of blues rock.

1989–2017: Varied Influence (“Gangsta of Love” through “Medley: The Joker/Three Little Birds”): The Steve Miller Band has inspired both “country bros” (Kenny Chesney, Tim McGraw, etc.) and “chill bros” (Dave Matthews, John Mayer, etc.). But Miller’s influence has shown up in further-flung places, too: aughts indie rock, nineties rap samples, Jamaican pop, and Space Jam.

Listen to it here: