  We review some recent developments in the subject of quantum corrections to
soliton mass and central charge. We consider in particular approaches which use
local densities for these corrections, as first discussed by Hidenaga
Yamagishi. We then consider dimensional regularization of the supersymmetric
kink in 1+1 dimensions and an extension of this method to a 2+1-dimensional
gauge theory with supersymmetric abelian Higgs vortices as the solitons.
