  Boundary conditions and defects of any codimension are natural parts of any
quantum field theory. Surface defects in three-dimensional topological field
theories of Turaev-Reshetikhin type have applications to two-dimensional
conformal field theories, in solid state physics and in quantum computing. We
explain an obstruction to the existence of surface defects that takes values in
a Witt group. We then turn to surface defects in Dijkgraaf-Witten theories and
their construction in terms of relative bundles; this allows one to exhibit
Brauer-Picard groups as symmetry groups of three-dimensional topological field
theories.
