Domain walls are the transition regions between two magnetic domains. These objects have been very relevant during the last decade, not only due to their intrinsic interest for the development of novel spintronics devices, also because of their fundamental interest. They can be nucleated in ferromagnetic nanostrips and can be driven by conventional magnetic fields and spin currents due to the injection of electrical pulses, which make them very promising for technological applications of recording and logic
devices. In this review, based on full micromagnetic simulations supported by a one-dimensional model, we describe the static and dynamics properties of domain walls in thin ferromagnetic and ferrimagnetic wires with perpendicular magnetic anisotropy. The aim of the present chapter is to provide a fundamental description of the numerical tools and the models which allow to describe the DW dynamics in previous and future experimental setups.
