Line defects in a topological phase correspond to surface defects in
a three-dimensional topological field theory. The classification and
properties of such defects, as well as of the point-like defects at
which they end, can therefore be studied in the framework of
topological field theory. Among the structures emerging in such an
analysis are module and bimodule categories over fusion categories.
Investigating these structures also provides structural insights, e.g.
there turns out to be an obstruction (taking values in the Witt group
of modular tensor categories) to the existence of defects, and
symmetries of the bulk theory can be related to the transmission of
bulk excitations through invertible defects.
As an illustration, I will present a few specific results for twist defects
in topological multilayer systems.