How to watch Blue Exorcist
Blue Exorcist needs a route decision because the 2011 season moved into an anime-original ending while later seasons returned to the manga storyline. The clean continuity route uses the early Season 1 setup, then Kyoto Saga, Shimane Illuminati Saga, Beyond the Snow Saga, and The Blue Night Saga. You can still watch the rest of Season 1 as an alternate conclusion; just do not expect Kyoto to preserve every event from that branch. Blue Exorcist: The Movie is another optional anime-original story and works best after the first season rather than between later canon sagas.