It wasn’t far into its first season in 1975 that Saturday Night Live established itself as a musical tastemaker as well as a laugh factory. Since then, its become a platform for amazing introductions to new artists like Sam Smith, who made his U.S. late night debut at studio 8H, as well as a place for long-established legends to perform profound sonic nostalgia, like Jay-Z’s career-spanning medley or Mick Jagger’s trip through the Stones catalog.

On the eve of its 41st season premiere — which will feature Miley Cyrus as its host and musical guest— we remember our 41 favorite performances, listed below in chronological order.

Simon and Garfunkel, medley (1975)

Simon and Garfunkel broke up in 1970, but reunited multiple times over the years — including this performance on SNL when Simon hosted the show’s second episode ever in 1975. The duo engaged in some sibling-like banter (“Movies are over now?” Simon teased Garfunkel, who appeared in two films after their break-up) before launching into a serene medley of “The Boxer,” “Scarborough Fair,” and that year’s “My Little Town.” Although they weren’t exactly lovey-dovey, the two did occasionally exchange knowing smiles throughout the performance, gestures that hinted the two maybe weren’t as over as they seemed. —Ariana Bacle

Patti Smith, “Gloria” (1976)

Smith featured the Them cover on her debut album Horses, but it’s easy to forget she didn’t write the song (though she re-wrote the verses drastically) when watching her stripped-down performance during SNL’s first season.—Madison Vain

Joe Cocker and John Belushi, “Feeling Alright” (1976)

No one talks about the brass tacks that underpinned this seminal SNL performance: The shimmering blues guitar solos, the tight three-way backing harmonies, the punchy horns. That’s because John Belushi’s Joe Cocker impression (and startlingly good vocals!) provided the blueprint for every subsequent marriage of comedy and music on the show. —Eric Renner Brown

Elvis Costello, “Less Than Zero” and “Radio Radio” (1977)

Elvis Costello’s record label wanted him to play “Less Than Zero,” a single addressing a controversial British politician, on his SNL debut. He didn’t. So Costello and The Attractions played three bars of it, before the frontman turned around and waved them off. “I’m sorry, ladies and gentlemen, there’s no reason to do this song here,” he told the crowd. He then encouraged his bandmates to play the more up-tempo “Radio Radio.” The stunt prompted the show to ban Costello for over a decade. He eventually returned in 1989.—Will Robinson

Blues Brothers, “Soul Man” (1978)

​The Blues Brothers were the first of SNL‘s creations to move to the big screen, but the John Belushi and Dan Aykroyd-led band was legit. Their final performance on the show started the season 4 episode, with a lively rendition of Sam & Dave’s “Soul Man.” Seeing Elwood and Jake go from stillness to unhinged boogying is timelessly entertaining. —WR

Kate Bush, “The Man With the Child in His Eyes” (1978)

Kate Bush made her American television debut on SNL wearing a glittery gold bodysuit and crooning straight into the camera with varying looks of pleading desperation and wide-eyed delight. Her performance of the dramatic “The Man With the Child in His Eyes” showed off her vocal range, as well as her ethereal dance moves — mostly done while sitting crisscross on a grand piano. —AB

Prince, “Partyup” (1981)

SNL‘s sixth season was a mild disaster comedy-wise—most of the cast and writers from the previous year exited in solidarity with burned-out founder Lorne Michaels—but was a great leap forward for music. It expanded its reach beyond shaggy boomer rock into the worlds of funk and R&B and featured the SNL debuts of both Aretha Franklin and James Brown. Prince also made his first appearance that year, lending his carnal falsetto to a breathlessly kinetic rendition of the Dirty Mind album-closer “Partyup.” —Kyle Anderson

Queen, “Crazy Little Thing Called Love” (1982)

The British rock band got down to business on the SNL stage with a high-powered take on their 1979 rockabilly classic. Freddie Mercury stylized the track with some Elvis-like vibrato and snapped along to cowbell provided by drummer Roger Meddows Taylor. The frontman continued to hop around the stage, and passed the torch to Brian May for an energetic solo towards the set’s end. —Dana Rose Falcone

Run DMC, “Hit It, Run” (1986)

The pioneering Queens-bred hip-hop crew broke down many barriers and went were no MCs had gone before. Not only were Run DMC the first rappers to perform live on MTV, but they also popped SNL’s rap cherry when they tore through a particularly fierce version of their crossover smash “Walk This Way.” But the hip-hop era really arrived at 30 Rock when Malcolm-Jamal Warner tossed to them a second time and they busted out “Hit It, Run,” as pure a two-turntables-and-a-microphone jam as there is. —KA

Paul Simon with Ladysmith Black Mambazo, “Diamonds on the Soles of Her Shoes” (1986)

Simon continued to be an SNL stalwart. To celebrate the release of his chart-busting and Grammy-winning comeback album Graceland, Simon showed up in 1986 with South African choral group Ladysmith Black Mambazo for the warm, lilting single “Diamonds on the Soles of Her Shoes,” an exceptional song given an even better spectacle. —KA

The Replacements, “Bastards of Young” (1986)

To be clear, there is nothing great about The Replacements SNL debut, but that’s what makes it great. The Minneapolis rockers took over the studio and delivered an out-of-tune, bumbling, hard-to-hear, drunken take on their track “Kiss Me on the Bus.” Producers were none too pleased and the group received a lifetime ban from studio 8H. —MV

The Sugarcubes, “Birthday” (1988)

Are you looking closely? Did you hear Matthew Broderick say, “All the way from Iceland”? That’s right, it’s Baby Björk! The now-star made her SNL debut fronting alt-rockers The Sugarcubes as they crossed the Atlantic to kick off their first tour. Cascading over a tornado of sonics — aggressive bass, sharp guitar, peaking horns — Bjork’s voice is otherworldly and surreal in its command. —MV

Neil Young, “Rockin’ In the Free World” (1989)

Neil Young isn’t a showman, which might be what makes his performances so enthralling. The grunge-before-grunge rocker donned a leather jacket and torn jeans to play his Reagan-era indictment—which appropriated George H.W. Bush’s “thousand points of light” line in scathing fashion—”Rockin’ In the Free World” on the season 15 premiere. No frills, all distortion, this performance is just as vital today as it was 26 years ago. —ERB

Mariah Carey, “Visions of Love” (1990)

After being introduced by host Patrick Swayze, Mimi took the Saturday Night Live stage for the first time in October 1990. Fresh off the release of her self-titled studio album, Carey impressed with a stunning performance of “Visions of Love,” her debut chart-topping single. In a perfectly ’90s jean jacket and perm, Carey hit all the high notes as only she can.—Madeline Boardman

Robyn, “Call Your Girlfriend” (2011)

Complete with backwards flips, gyrations on the floor, and excellent hip shaking, the queen of dance-pop electrified SNL with her upbeat vocals and high-energy stage presence. And when the electro breakdown kicked in, Robyn delivered some futuristic moves before taking to her knees for the final chorus. —DRF

Mick Jagger with Jeff Beck and members of the Strokes, Arcade Fire, and Foo Fighters (2012)

In the 2012 SNL finale, Jagger welcomed Arcade Fire, Foo Fighters, Jeff Beck, and Nikolai Fraiture of the Strokes to perform with him. Arcade Fire and Fraiture joined him for a trip through the early Stones’ single “The Last Time,” the Foos joined him for “19th Nervous Breakdown” and “It’s Only Rock ‘n Roll (But I Like It),” and Beck joined him for the final song, an original blues composition. It was as decadent as it sound. —MV

Frank Ocean, “Pyramids” (2012)

John Mayer joined Frank Ocean onstage to show off his guitar skills during an abbreviated version of “Pyramids,” a track off Ocean’s beloved debut studio album. Ocean’s vocals are as clean and sensual as they are on the record itself, and Mayer hangs in the background until it’s time for him to shine with a guitar solo that is both moving and amusing: The nearly minute-long solo is worth replaying solely for his animated facial contortions. And Ocean doesn’t just sit around while Mayer gets the spotlight — he plays one of the multiple arcade games dotting the stage until the song ends and he gives the camera a pleased smile. —AB

Kanye West, “Black Skinhead” (2013)

Few performers could have prompted Oscar winner Ben Affleck to concede that West was “the man you came to see.” West has used SNL as his platform to introduce his new aesthetic (see: the AutoTuned depression of 808s & Heartbreak; the self-aggrandizing rich My Beautiful Dark Twisted Fantasy). The rollicking drums of “Black Skinhead” debuted and were complemented by visuals three hellish dogs, a “NOT FOR SALE” sign, and black KKK members. The message was clearer upon the album’s release: Say hello to Yeezus. —Will Robinson

Arcade Fire, “Afterlife” (2013)

Decked out in all-white formalwear, the Canadian band debuted what turned out to be one of Reflektor‘s most affecting tracks on a Tina Fey-hosted episode of SNL. “Afterlife” showcases everything Arcade Fire does well, and it does it in one five-minute song: the poignant lyrics, the calm opening building to a desperately danceable chorus, the urgent drums, the musical interplay between founders (and spouses) Win Butler and Régine Chassagne. This performance proved Arcade Fire had another emotional sing-along staple like “Wake Up” in them — and that this was it. —AB

Sam Smith, “Stay With Me” (2014)

Taking the stage just months after the release of his debut album, the singer made his SNL debut with a passionate version of radio sweetheart “Stay With Me,” backed by an orchestra and mini gospel choir. A then 22-year-old Smith also performed a sultry, striped down rendition of “Lay Me Down,” during which the London native proved why he bests the new generation of singer/songwriters, all while holding back tears. —DRF

St. Vincent, “Birth In Reverse” (2014)