This paper reviews the Gerchberg-Saxton algorithm and variations thereof that have been used to solve a number of difficult reconstruction and synthesis problems in optics and related fields. It can be used on any problem in which only partial information (including both measurements and constraints) of the wavefront or signal is available in one domain and other partial information is available in another domain (usually the Fourier domain). The algorithm combines the information in both domains to arrive at the complete description of the wavefront or signal. Various applications are reviewed, including synthesis of Fourier transform pairs having desirable properties as well as reconstruction problems. Variations of the algorithm and the convergence properties of the algorithm are discussed.