In the last years modern mathematical methods for the solution of boundary value problems (BVPs) attracted much interest in Geodesy, namely the finite difference method (FDM), the finite element method (FEM), and the boundary element method (BEM). They are able to solve general linear BVPs directly, i.e. up to any desired numerical precision. We could then abolish several doubtful classical geodetic approximation steps like spherical and constant radius approximation.