The standard theory for the description of cosmic rays is the quasilinear theory. Whereas it was assumed for a long time that quasilinear theory is a reliable and useful tool to describe transport of charged particles; recent test-particle simulations have demonstrated that for certain parameter regimes a linear description of transport is not appropriate. It is the purpose of this paper to present a rigorous comparison between quasilinear theory and previous test-particle simulations. We demonstrate that quasilinear theory is invalid, or at least inaccurate, for parallel and perpendicular transport for the most parameter regimes if a magnetostatic model is assumed. We also demonstrate that recent nonlinear theories are able to reproduce at least some of these simulations. Furthermore, we reformulate the recently proposed NLGC theory for perpendicular transport to describe diffusion in isotropic magnetostatic turbulence.