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