The first nonlinear image restoration algorithms were devised a little more than a decade ago. The subsequent development of this subject by a number of research workers has produced a rich and fascinating literature. But because much of it is located in unfamiliar journals and publications, many astronomical newcomers to the field may be unaware of this work. It has been known since the discovery of the nonlinear image restoration techniques that they have pronounced performance advantages over linear restoration techniques in astronomical applications, and many of the published examples of nonlinear restorations of imagery have involved astronomical data. The new image detector systems appearing in optical astronomy, particularly CCDs, produce images of a quality that fully justifies the employment of sophisticated algorithms for the extraction of the maximum amount of information from the data. This review of the literature has been prepared in the hope that it will encourage new astronomical workers to enter into it.