I will begin with recalling some basic facts about stacks. Particularly interesting are smooth stacks describing singular spaces. There is a close connection to other models like Lie groupoids and orbifolds. However regarding sheaves these models differ from stacks. I will talk about how to relate sheaves on a smooth stack to sheaves on its Lie groupoid atlas. This allows treating symplectic geometry in a nice way. As an application I will transport Fedosovs deformation qualtization and Delignes classification from smooth manifolds to smooth stacks. As an example I will quantize the moduli of flat connections with orbifold singularities.