Marine reptiles were the ocean-going counterparts to the dinosaurs. As they are reptiles, they breath air. It is a wide group, containing Ichthyosaurs, Pliosaurs and Plesiosaurs, Mosasaurs, Nothosaurs, and several others.
Though this group contains any reptile that lives in the sea (Sea Snakes, Sea Turtles, Marine Crocodiles, Etc.), it is usually used only in reference to the former extinct groups.