The Muppets, is the twelfth film to feature Jim Henson's iconic title characters as the stars. Here's a quick rundown of the earlier installments to help catch everybody up.
NOTE: The two films from 2002, It's A Very Muppet Christmas Movie and Kermit's Swamp Years, are not included on account of I haven't seen either in their entirety.
The Muppet Movie (1979)
The original film is still, after all these years, frequently regarded as not only the best Muppet film but also the best Muppet-related production, period. I can't really argue otherwise. Billed as a (loose) prequel to the Muppet Show series, it's the story of banjo-strumming Kermit's departure from the swamp to seek fame and fortune in Hollywood, picking up a motley crew of similarly-inclined pals and battling the machinations of a sinister fast food entrepreneur along the way. Of all the films, this is the one that best captures the uniquely-70s vibe of the series; one part wacky puppet comedy, one part vaguely-grimy 70s road movie, one part totally sincere quest-for-enlightenment epic.
In a way, the film is like the apotheosis (or the last defiant gasp) of the starry-eyed flower child ethos of the late 60s that had infused Jim Henson's work and persona from the beginning but was otherwise teetering on the brink of pop culture oblivion at the time the film was coming out - the story of a collection of shaggy, silly, idealistic misfits surviving a psychedelic journey through Americana en route to immortality via the entertainment biz.
The Great Muppet Caper (1981)
Film #2 was more of a straightforward satire of mystery movies, with Kermit, Fozzie and Gonzo as reporters who get wrapped up in a case of mistaken identity and jewelry theft. These days it tends to take some hits for focusing more on physical comedy than the wordplay that had characterized the earlier film, but it's exceptionally paced and features one of the more interesting versions of Miss Piggy, who probably undergoes the most drastic character shifts from film to film of any "main" Muppet. It also features the famous bike-riding scene, which is among the most technically complicated sequences Henson's team ever put together.
The Muppets Take Manhattan (1984)
The final installment of what's generally thought of as the original/classic Muppet Trilogy goes back to the more genial "grownup-movie-but-with-silly-puppets" feel of the original, dropping the cast into a semi-retread of the first film's stardom search narrative with Broadway replacing Hollywood, infused with the post-Woody Allen "rebirth of the Empire City" vibe of mid-80s New York. This time, Kermit and company are college graduates trying to get their variety act turned into a Broadway show, complicated by a character-scattering breakup and an amnesiac Kermit briefly transformed into a yuppie ad executive.
Poking fun at showbiz had always been part of the Muppets bread and butter, but this is easily the most "inside" example of that particular streak of humor, with lots of jokes about production politics, script pitches and industry nepotism in between the more general "because it's New York" stuff. One memorable extended cutaway expanded the Muppet Universe by introducing The Muppet Babies. That one bit went over so well that it was turned into an above-average animated spinoff that introduced a whole generation to the wonder of cartoon characters interacting with popular movies and public-domain film clips.
This would be the last (theatrical) Muppet feature completed before Jim Henson's death, and marks the solo directing debut of Muppet performer (and voice of Yoda) Frank Oz, who went on to have a tremendously successful post-Muppets career in "regular" movies.