The Loewner framework and transfer functions of singular/rectangular systems. A connection is established between the Loewner framework for model reduction and the generalized inverses of singular and rectangular matrices. In this context both the Moore-Penrose and the Drazin inverses are involved. As a consequence this approach yields transfer functions for singular and rectangular systems. Thus the Loewner framework constitutes a natural and direct way for constructing models from measured input/output data.