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Plesiosaurus is the eponymous member of the group of marine reptiles known as plesiosaurs, which were characterized by their sleek bodies, wide flippers, and relatively small heads set at the end of long necks. These Jurassic reptiles were once famously described as looking like "a snake threaded through the shell of a turtle," although it was later established that they didn't have shells.
There's a lot we still don't know about Plesiosaurus, which like many "name brand" prehistoric reptiles is less well understood than the family it gave its name to (for a terrestrial parallel, think of the enigmatic Hadrosaurus and the well-known family of duck-billed dinosaurs, the hadrosaurs). Discovered very early in paleontological history (by the pioneering naturalist Mary Anning), Plesiosaurus created a sensation back in the early 19th century, scientists (and, to a slightly lesser extent, the general public) not quite knowing what to make of it.
Plesiosaurs in general (and Plesiosaurus in particular) probably weren't the most accomplished swimmers, since they lacked the hydrodynamic shapes of their bigger, meaner and more streamlined cousins, the pliosaurs. It's currently unknown whether Plesiosaurus lumbered onto dry land to lay its eggs or gave live birth to its young while still swimming.