The best overseas shows are often the ones that don't make it to Britain. Or if they do, they end up being tucked away on some obscure channel and barely promoted. Community, a college campus comedy that throws out the sitcom rulebook, is the latest to join this growing list of great shows – Freaks and Geeks, Party Down, Mr Show – that you're probably only going to see on box set.

You can kind of understand why this US show has been ignored. Anyone who caught the first episode could be forgiven for not watching further: it's funny enough, but hardly that special, and not all that typical of what followed. Disbarred lawyer Jeff has to attend community college to get the qualifications he has been caught lying about. As a scam to get to know pretty fellow student Britta, a vaguely right-on activist type who had previously dropped out of education, he sets up a fake Spanish study group. This backfires when others turn up for some actual study: a mixed bunch including Shirley, a very Christian single mother; Pierce, a casually racist and sexist tycoon, who made a killing in moist towelettes; and Troy, who was a quarterback at high school.

But don't go thinking this is a sitcom about a wisecracking lawyer learning valuable life lessons from goofy misfits. While that's a setup that would keep many a sitcom going, for a while anyway, Community is about much more. If you like your sitcoms formulaic, this isn't the one for you. Perhaps more than any other, Community messes with the format, pushing sitcom into strange territory. They've had an all-puppet animated episode, an amazingly authentic action-movie pastiche, a zombie episode, as well as ones that riff off Goodfellas, Apollo 13 and – quite wonderfully – the 1981 Louis Malle movie My Dinner With André. They've even dealt with parallel universes. That it manages all this with the same seven core characters in the same location makes it all the more remarkable.

While much of Community's strength is derived from its incredibly productive writers, it's the cast who surprise and delight. The big names are Joel McHale as Jeff, famous for not being an actor, since he's also the host of sarcastic TV round-up show The Soap; and Chevy Chase, who is famous for being very funny two decades ago, and plays Pierce here. The others carry almost no baggage at all. Alison Brie, who plays Pete Campbell's frumpy wife Trudy in Mad Men, is so impossibly cute here as Annie, it kind of ruins Mad Men for you. With her at home, you wonder why Pete would ever stray.

Everyone gets a chance to shine. The show's secret weapon, its biggest surprise, is Danny Pudi's as Abed, a Palestinian-Polish-American who treats life as a TV show. He provides voiceovers, meta-references to what the show is about, and whatever sitcom tropes (will they/won't they, guest stars, etc) the episode is deconstructing. Pudi makes his character neither a cypher nor a typical nerd: he's simply incredibly likable and frequently the coolest person in Community. But pick your own favourites from one of the smartest, sharpest and funniest shows you're unlikely to see on TV. Phelim O'Neill