  We review recent work on a new class of topological defects which possess a
nonsymmetric core. They arise in scalar field theories with global symmetries,
U(1) for domain walls and SU(2) for vortices, which are explicitly broken to
$Z_2$ and U(1) respectively. Both of the latter symmetries are spontaneously
broken. For a particular range of parameters both types of defect solutions are
shown to become unstable and decay to the well known stable walls and vortices
with symmetric cores.
