  We study what might be called fractional vortices, vortex configurations with
the minimum winding from the viewpoint of their topological stability, but
which are characterized by various notable substructures in the transverse
energy distribution. The fractional vortices occur in diverse Abelian or
non-Abelian generalizations of the Higgs model. The global and local features
characterizing these are studied, and we identify the two crucial ingredients
for their occurrence - the vacuum degeneracy leading to non-trivial vacuum
moduli M, and the BPS nature of the vortices. Fractional vortices are further
classified into two kinds. The first type of such vortices appear when M has
orbifold Z_n singularities; the second type occurs in systems in which the
vacuum moduli space M possesses either a deformed geometry or some singularity.
These general features are illustrated with several concrete models.
