Many physical phenomena are modeled by partial differential equations (PDEs) that cannot be solved analytically anymore. Thus our aim is to compute a - hopefully - reliable approximation of the solution to such a PDE. One of the basic steps is to transfer the infinite-dimensional problem to something that computers - with finite memory - can handle. In this "What is..." talk, we will get an idea how the Galerkin Finite Element Method (FEM) serves this purpose. In the end, we shall also see a special variant, namely the Discontinuous Galerkin (DG) method, and discuss its uses.