Finite element methods are one of the most widely studied and broadly employed means for the numerical approximation of the solution to PDEs in practical application settings. While finite element methods over simplicial and cubical meshes are becoming increasingly standardized across disciplinary boundaries, there is a booming interest in the definition and implementation of finite element methods over unstructured meshes of generic polygons and polyhedra. In this talk, I will provide a brief overview of this "zoo" of methods (including virtual elements, weak Galerkin, and hybrid higher order) and will discuss some of my contributions in the arena of generalized barycentric coordinate methods.