Studies on the retrieval of a complex function from data on its modulus and the modulus of its Fourier spectrum are briefly reviewed. An analog optical method of solving this same problem is described. Pictorial explanations are presented concerning the ambiguity of the retrieval of a spectrally bounded one-dimensional function from a single modulus. Some methods of retrieval of time characteristics of radiation are analyzed from the standpoint of the phase retrieval problem that rests on spectral measurements or on measurements of the autocorrelation function.