Erased is a psychological, time-traveling thriller produced by A-1 Pictures and Aniplex. Atsuhiro Iwakami and Kiyoko Matsuzaki are chief producers on the show. Erased is about a man, Satoru, who, at seemingly random times, is reverted back in time a few moments in order to prevent a tragedy from occurring. This plays into the fact that he constantly dwells and feels guilty about a specific instance in his childhood when three of his classmates were murdered, and feels as though he could have made a difference if he just reached out to one of them. After a particularly traumatic experience (no spoilers), his power takes him back to his childhood and with the knowledge of the future, plans how he is going to save the lives of his classmates. I find this series, specifically as an anime, to be refreshing because it doesn't over-emphasize nor over-explain Satoru's time-traveling ability. It simply uses it as a storytelling mechanic to amazing effect.
https://www.youtube.com/watch?v=DwmxEAWjTQQ