The Factorization Method (FM) is a sampling method for solving certain kinds of inverse problems where a geometric parameter (i.e. a domain) has to be determined. Since the first presentation by Andreas Kirsch in 1998 for inverse acoustic scattering by sound-soft and sound-hard objects, the factorization method has been generalized to many other applications in inverse scattering theory and impedance tomography.

A striking feature of the Factorization method is its sound theoretical foundation together with its simple and fast implementation. A short history of the factorization method will be given in this talk. Included are a sketchy summary of the existing results and some meaningful discussions. Furthermore, we list some interesting open problems.