The motion of magnetic domain walls is a case study for the dynamics of magnetization. It is by essence of precessional nature, described by torques arising from magnetic field or interaction with a spin-polarized current. This has been the subject of intense research efforts in the past two decades. While new physics keeps being continuously uncovered, it is now well established that the magnetization profile of a domain wall, and even more its topology, are crucial in determining its dynamics.
In the first part of my presentation, I will review the background of this field, ranging from the fundamental physics of precessional dynamics of magnetization and the mechanisms of domain wall motion, to some motivations for applications. In the second part, I will report some of our results of domain wall motion in cylindrical nanowires. In contrast with most of the systems studied to far, made by thin-film deposition and therefore rather thin and flat, the consideration of cylindrical nanowires allows the emergence of a new topology of domain walls, largely pushing upwards the usual limits for domain-wall speed. This brings us now close to a new regime proposed theoretically however not observed yet, which is the dynamic coupling between domain walls and spin waves when their speed and phase velocity coincide.