The self-organized emergence of spatio-temporal patterns is a ubiquitous phenomenon in nonlinear processes on large domains. In this talk the Landau-Lifshitz-Gilbert-Slonczewski equation is studied from this viewpoint, highlighting various aspects of the theory. The model describes magnetization dynamics in the presence of an applied field and a spin polarized current. Here we consider the case of axial symmetry and focus on one space dimension. This is joint work with Christof Melcher (RWTH).