The principal approaches to random-access file organization and addressing are reviewed in this paper. The review is general, in the sense that it is relatively independent of specific equipment. In the case of a number of unsettled questions, the author's evaluations of alternatives are included. The relation between sorting and random-access file addressing is clarified by reviewing both as belonging to a common class of ordering operations. Basic considerations of both sequential and random-access approaches, arithmetical key-to-address transformation methods with their overflow problems, and table lookup methods are discussed. Results of an experimental analysis of key transformation techniques are presented.