With the setup between Aniplex USA and Funimation now, the first series and Blue Exorcist: Kyoto Saga have now both been added to the Funimation site for streaming.
Each season is available in its Japanese with English subtitles form as well as its English language dub.
Normally, these two dimensions would never intersect, but having possessed all material substances, the demons are now intruding on the material world.