The Stokes and Navier-Stokes problems formulated on surfaces present a number of challenges distinct from those encountered for the corresponding Euclidean equations. In the context of numerical methods, these include the inability to formulate standard surface finite element velocity fields which are simultaneously continuous (H1-conforming) and tangential to the surface. In this talk we will give an overview of various finite element methods that have been derived for the surface Stokes problem, along with their advantages and drawbacks. We will then present a surface counterpart to the Euclidean MINI element which is the first FEM for the surface Stokes problem which does not require any penalization. Finally, we will briefly discuss extension to other nodal Stokes FEM such as Taylor-Hood elements. This is joint work with Michael Neilan.