B-type defects in Landau-Ginzburg models

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.