I will discuss Landau-Ginzburg models with possibly different
superpotentials glued together along one-dimensional defect lines.
Defects preserving B-type supersymmetry can be represented by matrix
factorisations of the difference of the superpotentials. The composition
of these defects and their action on B-type boundary conditions is desribed
in this framework. As an example I will discuss N=2 minimal models and
compare to results from conformal field theory.