  We review our work of the past decade on one-loop quantum corrections to the
mass M and central charge Z of solitons in supersymmetric field theories: the
kink, the vortex, and the monopoles (focussing on the kink and the monopoles
here). In each case a new feature was needed to obtain BPS saturation: a new
anomaly-like contribution to Z for the kink and the N=2 monopole, the effect of
classical winding of the quantum vortex contributing to Z, surface terms
contributing to M of the N=4 monopole and to Z of the N=2 and N=4 monopoles,
and composite operator renormalization for the currents of the "finite" N=4
model. We use dimensional regularization, modified to preserve susy and be
applicable to solitons, and suitable renormalization conditions. In the mode
expansion of bosonic and fermionic quantum fields, zero modes appear then as
massless nonzero modes.
