  We discuss general properties and possible types of magnetic vortices in
non-Abelian gauge theories (we consider here $G= SU(N), SO(N), USp(2N)$) in the
Higgs phase. The sources of such vortices carry "fractional" quantum numbers
such as $Z_n$ charge (for SU(N)), but also full non-Abelian charges of the dual
gauge group. If such a model emerges as an effective dual magnetic theory of
the fundamental (electric) theory, the non-Abelian vortices can provide for the
mechanism of quark-confinement in the latter.
