The Muppet Theatre is the setting for The Muppet Show, where it was first established over the course of five seasons of television. It is a grand old vaudeville house that has seen better days, but still manages to suit the showbusiness needs of the Muppets.
The building's exterior is first seen in the series' coda, The Muppets Go to the Movies, where the camera pans back from the stage, out the front doors, and provides a full view of The Muppet Theatre name on the building. Kermit the Frog serves as a house manager to the theatre which is owned by Scooter's uncle J.P. Grosse (a fact Scooter is often happy to reiterate with his amphibious boss).
According to a 1991 storybook, the theatre was built by a stage actor named John Stone in 1802. In The Muppet Show episode 106, Kermit identifies the structure as The Benny Vandergast Memorial Theatre, but following the Muppets' residency, The Muppet Theatre name becomes prominently displayed on advertising posters and backstage signs. The British spelling of Theatre can be attributed to its location in London; while locking up the doors at the end of The Muppets Go to the Movies, Miss Piggy asks Kermit to walk her to The Tube, London's subway system ("I love to walk to The Tube!", she exclaims).
After The Muppet Show, the location of The Muppet Theatre becomes more ambiguous; either as a result of renting playhouses in different cities, or through the magic of the Muppets' inconsistent continuity. Most stage areas occupied by the Muppets are either called The Muppet Theatre in name or bear some resemblance to the their original home on The Muppet Show. For example, commercials for Polaroid, The Muppets Celebrate Jim Henson, Weezer's "Keep Fishin'" music video, and others, are close facsimiles of the original theatre (sometimes with modifications), and are most likely meant to serve as such.
It's a Very Merry Muppet Christmas Movie clearly establishes a theatre located in New York City, as Piggy's apartment (in an alternate universe) has a view of the twin towers of New York's World Trade Center. The plot of the TV movie involves the theatre being in jeopardy of finding itself repurposed as a night club. Its owner's plan is ultimately foiled by Pepe the King Prawn when he registers the theatre as an historical landmark; the document uses the Americanized spelling, The Muppet Theater.
A third definitive location was established in the 2011 film The Muppets, where it's situated within the Muppet Studios lot in Hollywood. The El Capitan Theatre served as The Muppet Theatre exterior during filming, returning the name to its British spelling, The Muppet Theatre. This version of the theater was used in Muppets Most Wanted and a promotional ad for Orange.
