  This note is intended as an introduction to the functorial formulation of
quantum field theories with defects. After some remarks about models in general
dimension, we restrict ourselves to two dimensions - the lowest dimension in
which interesting field theories with defects exist. We study in some detail
the simplest example of such a model, namely a topological field theory with
defects which we describe via lattice TFT. Finally, we give an application in
algebra, where the defect TFT provides us with a functorial definition of the
centre of an algebra. This involves changing the target category of commutative
algebras into a bicategory. Throughout this paper, we emphasise the role of
higher categories - in our case bicategories - in the description of field
theories with defects.
