  We consider 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 described in this framework. The cases of
Landau-Ginzburg models with superpotential W=X^d and W=X^d+Z^2 are analysed in
detail, and the results are compared to the CFT treatment of defects in N=2
superconformal minimal models to which these Landau-Ginzburg models flow in the
IR.
