The dynamic properties of magnetic domain walls in nanotubes and in cylindrical nanowires can be significantly different from the well known domain wall dynamics in thin films and in flat thin strips. The main differences are the occurrence of chiral symmetry breaking and, perhaps more importantly, the possibility to obtain magnetic domain walls that are stable against the usual Walker breakdown. This stability enables the magnetic field-driven propagation of the domain walls in nanotubes and nanocylinders at constant velocities which are significantly higher than the usual propagation speeds of the domain walls. Simulations predict that the ultrafast motion of magnetic domain walls at velocities in a range above 1000 m s-1 can lead to the spontaneous excitation of spin waves in a process that is the magnetic analog of the Cherenkov effect. In the case of solid cylindrical wires, the domain wall can contain a micromagnetic point singularity. We discuss the current knowledge on the ultrafast dynamics of such Bloch points, which remains still largely unexplored.