Last night, Saturday Night Live unveiled "Goodnight, Sweet Prince," a special show devoted to Prince, the iconic musician and erotic muse who died this week at the age of 57. Jimmy Fallon was the host for the special, introducing clips from Prince's various SNL performances over the years, and sharing personal anecdotes and footage of the performer as well.

"Other people may have been on the show more times, or performed more frequently, but there was always something different about a Prince performance. It was special, it was an event, it was Prince," Fallon, who got choked up at times during the special, said in the introduction. "Times have changed, styles have come and gone, but no matter what, Prince has never not been cool." You can watch the full special below.

The four SNL performances include Dirty Mind deeptrack "Partyup" from 1981 (when Prince was still opening for Rick James); "Electric Chair" from 1989 (with giant Batman logo in the background, since it came from the soundtrack); "Fury" and "Beautiful, Loved and Blessed" from 2006 (Prince gives a shoutout to "superstar" Mary Katherine Gallagher at the end of the latter performance); and a medley of "Clouds," "Marz" and "Another Love" from his 2014 performance during Chris Rock's episode.

After that, Fallon retold the story about Prince playing SNL's 40th Anniversary after-party, talking about being the unofficial MC and happily having to hold Prince's gloves as he performed "Let's Go Crazy" at 4:30 a.m. After learning from Dave Chappelle that Prince was in the house, Fallon dared him to come perform: "All of a sudden, the crowd parted," Fallon said. "It really was a cloud of purple smoke, and just kinda this dude floated, you just see this little afro floating toward you, and it's almost like he had rockets on his legs or something, he wasn't even walking...he floated to the stage."

"Every single person who was at this thing came rushing to the stage to watch this guy perform and destroy. And it's just so much joy and love and fun put into this thing. It was the greatest, coolest party you could even imagine. Imagine the Oscars and the Grammys, everything combined, that's what this party was."

Check out high quality, never-before-shared footage of that Prince performance below. You can see him surrounded by Haim, Chris Rock, Maya Rudolph, Martin Short, Bill Murray, Cuba Gooding Jr., Emma Stone, and more.

To close out the special, there were four sketches of "The Prince Show," with Fred Armisen as Prince. You can watch one of them, featuring Shia LaBeouf, below.

And finally, there's been an flood of excellent Prince live clips being put online (finally!), including this completely amazing 1985 Grammys performance of "Baby I'm A Star" that you need to see.