Erased tells the story of Satoru Fujinuma, a manga artist who occasionally has involuntary "revival" episodes where he repeats short periods of time. During those episodes, he can take action to avoid minor or major disasters. Then his most significant "revival" ever pushes him back eighteen years, with a chance to stop a string of serial murders at his elementary school. (Warning: Some spoilers below.)
That's a pretty interesting premise. I usually don't like time travel, because it's so easy to end up with a story that makes no logical sense, given the huge power that a time travel character has to work with. In this case, the involuntary nature of the "revival" power prevents that from being a significant factor. It's a little too convenient that Satoru ends up getting multiple chances to change the past, but that's a fairly minor quibble.
The story is largely a mystery-thriller, with Satoru working against an unknown killer to save the children that his future-informed-self knows are being targeted. Knowledge from the future only goes so far, though, as events change each time he does something different. Most of the series deals with his efforts to save Kayo, a girl who is isolated due to her abusive family situation and thus a prime target. Two (or three, depending on who you count) other victims are also saved, though that part goes by awfully fast compared to the time spent with Kayo.
Then things change entirely in the last two-and-a-half episodes, as Satoru meets the killer directly and changes the future significantly. There's one massive hole in the plot that was never explained to my satisfaction. This fifth-grade boy has discovered and thwarted a serial killer. The killer has the boy at his mercy, and appears to fully intend to kill him. We see the boy drowning with no one but the killer anywhere nearby. But somehow he survives (though in a coma), and we're never shown how it happens. The only explanation is that somehow the killer feels it's necessary that the boy lives, possibly because of a final shouted "I know your future" line as the water closes in. That just doesn't make any sense to me, even if you accept the "I need him alive" killer psychosis. Who cares about a dead kid knowing the future? He's out of the way now. Why the drowning in the first place, if the killer already knows he wants the boy alive? Why not lock him up in a basement or something? This sort of thing happens all the time in the sillier kinds of stories, I know. This one is supposed to be a mystery that makes you think, though, so it stands out as being poorly written.
That ridiculous bit aside, the wrap-up of the series isn't too bad. Everything turns out more or less for the best, with no one dead and the bad guy caught. The changed timeline is pretty rough on Satoru and his mother, but at least they stay alive and out of jail. It feels like a bit of a cop-out, though, with Satoru's miraculous survival. I think the ending would have felt much more complete as a story of sacrifice, where Satoru didn't escape, but the original victims were saved by his actions.
It's nice to watch a series that pretty much entirely avoids the most annoying anime stereotypes. There's no scantily clad girls, harem relationships, over-the-top emotional expressions, and so on. Big eyes are only for kids. In his adult time period, Satoru doesn't pursue the high school girl that he works with (despite multiple opportunities) until the very end when she's four years older. I appreciate not having to sit through all that.
Erased is a decent mystery story, despite the sub-par bits near the end. The characters are nicely developed, for the most part, and the production values are just fine. I think it's still worth watching, even if the ending isn't everything it could have been.