It took me ages to get around to watching this, because it's about a school music club. That reminded me of idol shows. However I'd also heard that it was very good, which indeed it is. It's lovely. A common criticism is apparently that it's not very interested in the progress of the band and their music, but I'm absolutely fine with that.
They're the Beatles reinvented as Japanese schoolgirls, by the way. Admittedly this isn't useful information, since the show becomes less enjoyable if you're watching it through a Beatles filter. Yui isn't John Lennon (for example) and she's less funny and interesting if you're trying to see her as some kind of John Lennon representation rather than just her own goofy self. Just think of it as inspiration. These are schoolgirls having a laugh. They're a million miles away from any kind of Beatles-level genius or fame and the only similarities are in their personalities. That said, though...
YUI HIRASAWA (guitar) = John Lennon, both being goofy, optimistic space cases. She's nicer than him, though, and fortunately didn't have his horrible childhood. She's not so stupid that her voice actress ever starts doing a moron voice, but she can be awesomely empty-headed. Like Lennon, she's full of natural talent but untrained (e.g. neither could ever read sheet music), being taught to play their guitars by...
MIO AKIYAMA (bass guitar) = Paul McCartney, both being left-handed, punctilious and prone to writing saccharine lyrics. Mio's more shy, though.
RITSU TAINAKA (drums) = Ringo Starr, like him being spontaneous and fun-loving. She's not an airhead (unlike Yui) but she has a gnat's attention span and those two girls are the goof-off squad.
TSUMUGI (MUGI) KOTOBUKI (keyboard) = George Harrison, although this is the most tenuous similarity. They're both quiet and sensitive, but Harrison wasn't a dozy, sheltered innocent with an insanely rich family that owned a mega-corporation. Mugi fantasises about things like eating hamburgers (which she's never done) and having a part-time job. She also seems to be a closet lesbian. Oh, and you wouldn't believe how she rocks that Audrey Hepburn look in the closing title sequence.
AZUSA (AZU-NYAN) NANAKO = Yoko Ono, but she brings the group together instead of splitting them up. She's also shocked by what a bunch of slackers, idiots and layabouts they are, which seems reasonable.
UI HIRASAWA = Yui's younger sister. The family's brains, practicality and good sense all went into Ui.
SAWAKO YAMANAKA = the teacher in charge of the music club, although they have to blackmail her into it. She's funny. She also has multiple faces: the sweet lady she pretends to be in public, the death metal rocker she used to be, the cosplay otaku fetishist she'll become at the drop of a hat...
So that's the cast! What's the plot? Um... not a lot, really. It's slice-of-life. The girls are looking for an after-school club. They somehow end up together, each for their own reasons, and before you know it they're eating cake, goofing around and getting shouted at by Mio for not practising enough.
I'd been expecting music club storylines, but no. The girls don't enter any competitions, don't really think about how to progress as a band and so on. (It's based on a four-panel manga from Manga Time Kirara, which might explain a few things.) Instead it's mostly just being funny and adorable, at which it's staggeringly good. It's so successful at that, in fact, that it helped to trigger the modern moe boom, which has made it detested by fans who blame it for drowning the anime industry in cute girl shows with no weight or substance. Mecha fans particularly hate it, apparently.
Even Tomoko liked this show, which staggered me since she has a very low tolerance for this kind of thing. (She liked it less on discovering the John Lennon link, though, since the sentiments implied by songs like Imagine, Give Peace a Chance and Happy Xmas (War Is Over) make her want to go out and stab people.) Returning to the show, incidentally, there's one paradoxical way in which these girls create more dramatic tension than you'd get in a more dramatic show. They're so dozy and skiving that they're capable of screwing up anything at any time. There's no such thing as plot-guaranteed success. However it's basically just happy and charming. Suitable for absolutely any audience, from babies upwards. This is the kind of gentle, lovable show that's enjoyable rather than a must-watch, but I'm looking forward to the rest of it enormously and I think the haters are silly.