  The spatial distribution of fields and currents in confining theories can
give direct evidence of dual superconductivity. We review the behavior of
vortices in the lattice Higgs effective theory. We discuss the techniques for
finding these properties and calculating the superconductivity parameters in
lattice simulations. We have seen dual Abrikosov vortices directly in pure U(1)
and SU(2) and others have also seen them in SU(3). We review the duality
transformation for U(1) in order to connect the U(1) results to a dual Higgs
theory.
  In the non-Abelian cases the system appears to be near the borderline between
type I and II. We also discuss the response of the persistent currents to
external fields.
