This talk is about topological solitons which arise in  magnetic materials whose energy includes a Dzyaloshinskii-Moriya interaction term in addition to the usual Dirichlet, Zeeman and anisotropy terms. After a brief review of static solutions I focus on the dynamics of magnetic skyrmions, also in the presence of an applied external current. I discuss  a geometrical proposal for approximating  the dynamics in terms of a finite number of collective coordinates, and compare the results of this approximation with numerical simulations.