The problem of phase retrieval, which arises in all experimental uses of diffracted electromagnetic radiation for determining the intrinsic structure of a diffracting object, is a question of the behavior of Fourier transforms of distributions on groups. For finite distributions, the problem can be solved by methods of factorization in suitable rings of polynomials. For continuous distributions with compact support, methods of complex analysis are used to solve the problem. In this paper the author discusses these methods and gives examples.