In this paper we present an overview of recent progress made in the understanding of the spintorque induced magnetization dynamics in nanodevices using mesoscopic micromagnetic simulations. We first specify how a spin-torque term may be added to the usual LandauLifshitz-Gilbert equation of magnetization motion and detail its physical meaning. After a brief description of spin-torque driven dynamics in the macrospin approximation, we discuss the validity of this approximation for various experimentally relevant geometries. Next, we perform a detailed comparison between accurate experimental data obtained from nanopillar devices and corresponding numerical modelling. We show that, on the one hand, many qualitatively important features of the observed magnetization dynamics (e.g., non-linear frequency shift and frequency jumps with increasing current) can be satisfactory explained by sophisticated micromagnetic models, but on the other hand, understanding of these experiments is still far from being complete. We proceed with the numerical analysis of pointcontact experiments, where an even more complicated magnetization dynamics is observed. Simulations reveal that such a rich behaviour is due to the formation of several strongly nonlinear oscillation modes. In the last part of the paper we emphasize the importance of sample characterization and conclude with some important remarks concerning the relation between micromagnetic modelling and real experiments.