Differentiable stacks are a class of singular spaces in differential geometry including orbifolds, leaf spaces of foliations and orbit spaces of Lie group actions. One possible definition is: a differentiable stack is a Morita equivalence class of Lie groupoids. It follows from this definition that geometry on differentiable stacks is more or less the same as Morita invariant geometry of Lie groupoids. Following this principle, several different geometries on differentiable stacks have been introduced and studied recently, including vector fields, differential forms, symplectic and Poisson structures, with several applications in Poisson Geometry and Mathematical Physics. In this talk, I will first review Lie groupoids, Morita equivalence and differentiable stacks. In the second part of the talk, based on joint work with A. Maglio, and A. Tortorella, I will briefly discuss contact structures on differentiable stacks.