  We present the analysis of the structure of fermionic vortices with the
spin-polarized core from a weak coupling limit to the unitary regime. We show
the mechanism for the generation of the {\it reversed circulation} in the
vortex core induced by an excess of majority spin particles. We introduce the
classification of the polarized vortices based on the number of Fermi circles
where the minigap vanishes. This provides a unique description of the vortex as
one cannot smoothly map wave functions into one another corresponding to
vortices differing by the number of Fermi circles. The effective mass of
quasiparticles along the vortex core is analyzed and its role in the
propagation of spin-polarization along the vortex line is discussed.
