Spin-transfer torque manifests itself in two main geometries, either submicrometer diameter pillars composed of magnetic multilayers, flooded by a current perpendicular to plane (CPP), or nanowires with current flowing in their plane (CIP). The first situation can be described rather well, from the magnetic point of view, in the framework of the macrospin model (see by Y. Suzuki). In the latter case, the typical situation is that of a magnetic domain wall under CIP current, with many internal degrees of freedom. In by H. Kohno and G. Tatara, a simplest model of the domain wall, called collective coordinates model, has been introduced to study this question. In this chapter, we will address the entire manifold of the degrees of freedom in the domain wall by micromagnetic numerical simulations, and apply this to the physics of CIP spin transfer in magnetic domain walls. We will consider soft magnetic materials only, where domain wall structures and dynamics are controlled by magnetostatics. This corresponds to the largest part of experiments that have been performed up to now, soft magnetic materials having generally lower coercive forces and domain wall propagation fields. The experimental counterpart to this chapter can be found in , by T. Ono and T. Shinjo. After briefly introducing micromagnetics and the typology of domain walls in samples shaped into nanostrips, we start by reviewing the field-driven dynamics in such samples. This situation was indeed considered first, historically, and led to the introduction of several useful concepts. Prominent among them are the separation between steady-state and precessional regimes, and the existence of a maximum velocity for a domain wall. The spin-transfer torque-induced domain wall dynamics will then be addressed, considering first the implementation of the CIP spin transfer torque in micromagnetics, with several components as introduced by theory. Comparison will be made to the field-driven case, with similarities and differences highlighted. In the nascent field of nanomagnetism and spintronics, micromagnetics can be considered to play the role of a translator. There are on one side experiments and on the other side theories about interaction between magnetization and spin-polarized electrical currents. Micromagnetics is a tool that translates the equations of the latter into quantitative predictions that can be compared to the former. Considering the present state of the subject of this book, with rapidly advancing experiments and theories, keeping in touch those two aspects of research is very important for its sound development. This is the objective of this chapter.