Abstract : I will present in this talk the basic principles of virtual-type Galerkin methods for the numerical approximation of PDEs. These methods have been introduced a few years ago. They are applicable on general polygonal/polyhedral meshes, and allow for arbitrary-order approximation. Salient examples of those methods are the so-called Virtual Element (VE) or Hybrid High-Order (HHO) methods. I will give some hints on the analysis of such methods, detail implementation aspects, and draw connections between those methods and some standard Finite Element or Finite Volume methods, as well as with some more recent schemes.