Over the last decade, there has been an exponential growth in interest and investigation of the problem of how best to conserve populations of endangered species. As a result, there is now a very extensive and widely scattered literature on this subject. Among recent papers which cite a large number of references are those of Boyce (1992), Ellstrand and Elam (1993) and Nunney and Campbell (1993). Soulé’s (1987) book gives a valuable survey of the subject, in which the chapter by Lande and Barrowclough (1987) deals with the population genetics of the problem. Much of this literature is concerned with the conservation of species where ex situ conservation is not a realistic alternative. The demographic and population genetics theory on which discussion of this broader issue is based, however, is also relevant to the special case of those species where the conservation of material in gene banks is possible. The purpose of this chapter is to give a brief outline of the population genetics theory on which discussion of in situ conservation is based and to introduce some of the terms and concepts used in the literature. We also indicate the kinds of experimental investigation of populations which are necessary to produce better recommendations about minimum viable population size than are possible at present.