Symplectic spinors were introduced by Kostant for geometric quantization. To define his spinors, he needed a metaplectic structure, a notion which is topologically the same as admitting a spin structure. This rules out important examples of symplectic manifold such as CP2. Dirac operators were defined in that context by Habermann. Rawnsley and Robinson showed how to use instead $Mp^c$-structures (the symplectic analogue of $Spin^c$) for which there is no obstruction. We shall recall what are those groups, how to construct and parametrize $Mp^c$-structures and define the corresponding Dirac operators.