I loved it. It'll probably end up being my favourite anime of the year. I've seen it called a romantic comedy, but the "comedy" part is understated and personally I'd call it a drama.
It is, though, controversial, both in Japan and the West. It's easy to find people who hate it. It's about a 26-year-old salaryman (Yoshida) who finds a schoolgirl (Sayu) on the street when coming home drunk late one night. She offers him sex in return for a place to stay. He's not into schoolgirls and bluntly refuses all her offers, but says she can sleep on his floor anyway. Sayu's 1200 km away from home and has been a teenage runaway for six months, sleeping with anyone who'll give her a roof over her head. She doesn't understand Yoshida at all and keeps trying to get him to take advantage of her until he flat-out orders her to stop. It's a weird sense of duty on her part, combined with an expectation of being kicked out again at any moment. "She's not trying to be modest. She can't take it, because she can't repay me. Why does a kid think like that?"
As for Yoshida, he's a stick-in-the-mud who seems twenty years older than his age. He can't do anything except by the book. He lets Sayu live in his flat and becomes her pseudo-guardian, buying things for her, waiting for her to pluck up the courage to go back home and yelling at her for being impressed that he's not a sleazebag. "Raise your standards!" He finds her sexy, yes, but he'll resist the temptation even when so drunk that he doesn't remember the next day.
POTENTIAL PROBLEMS WITH THIS SHOW
The premise sounds like hentai, even if the show determinedly rejects that. Yoshida's breaking the law. (A headline in ep.1 says, "Metropolitan Police arrested a man in Musashino for abduction of a minor on suspicion of kidnapping a 17-year-old girl.") Our heroes can't tell anyone where Sayu's living, so she can't attend school. Furthermore, she clearly has issues. It's easy for a certain kind of viewer to project their weird ideas on to her (e.g. "she has PTSD"... no, she doesn't), assert that the only way to fix Sayu would be years of therapy, identify with things that aren't there and so on. If you think Yoshida's denying Sayu the help she needs, you'll probably think he's despicable and that his friends are enablers. And you definitely won't enjoy the show.
It's a nerd fantasy scenario, including tame fanservice. A 16-year-old uses her cleavage and underwear to tempt a 26-year-old. Yoshida always refusing sex is actually part of the fantasy, because he's a Saintly Anime Protagonist.
Then we have the values. Family trumps everything and the correct place for Sayu is with her mother, even though the lady's a poisonous bitch who even at the end has only showed mild signs of thawing. People say "only your mother has the right", without ever asking whether her behaviour might have invalidated this supposed right. Is returning to live with her really a good idea? (Except on a material level, of course. Big house, lots of money, no longer a lawbreaker, can return to school, etc.) Similarly, Mishima's preaching is capable of crossing a line into you wanting her to shut up and piss off. "I was trying to help, but was I just doing the things I wanted to do?" You're vanishing up your own arse there, Yoshida. Also, an on-screen attempted rape is almost forgotten.
Yoshida's approach to Sayu can be described as "minimalist". There's a whole world of options he either ignores or doesn't consider. He never approaches police, family, therapists or a school. He never considers the "marriage" solution, which would have eliminated all their headaches (while admittedly being problematic in other big ways). He never wonders if Sayu might be on drugs and if he might one day find her gone and his flat stripped clean. Mind you, he never suspected a blatant possible lie in ep.1, so we know he's gullible.
Technically, the anime's middling. The animation's less sophisticated than it wanted to be to support the dialogue, e.g. Sayu's different smiles. That would have worked better in live-action, with real actors. (That said, though, the animation looks fine and it's full of subtleties to find on a rewatch, e.g. Sayu's little "ah" reaction on telling Yoshida her real name, which we'll understand better after ep.8.) As for the script, I'm a fan but it's driven by its pointed conversations, even when it slightly strains credibility in certain scenes that those two characters would be saying all that to each other just then.
Oh, and Gotou's decisions early in the show make her an idiot. Never had a boyfriend? Not surprised. She didn't exactly leap on her opportunities here.
WHY I LOVE THE SHOW ANYWAY
I like the people. I like their story and I wanted everything to work out for them.
I like the complicated, awkward resolution with the mother and her extremely half-hearted change. Maybe, possibly, perhaps. It's possible to disagree with a lot of the choices and assumptions that went into that... but the result is that Sayu and her mother no longer hate each other and have achieved some measure of reconciliation. That's more than most of us would have achieved in that situation. It's difficult, sure. It's not a Disney ending that makes everything perfect with a bow on top. (Will Sayu commit suicide one day, for instance?) Anyway: good. People are messy and I can believe in what was achieved here.
I like the subtlety of the portrayal of the characters. Little moments where the important thing goes unspoken and we've got to read the episode with our eyes, not our ears, e.g. when Yoshida finds Sayu attractive. Or the way Sayu's voice is mischievous.
I like everything Yoshida says in the last episode, for instance, which is exactly right and telling Sayu to do all the correct things. I like the bad decisions and annoying opinions of Sayu, Gotou and Mishima, which feel real to me. And, ultimately, I love this story because I'm a big soppy romantic.
It's worth pointing out, though, that after this came out, a man in Tokyo got arrested for having a schoolgirl living with him as here.