Originally, there was to be a published conference proceedings. Between the time of the Columbia meeting and its appearance in 1982, the volume's rationale, purpose, content, and editorship have changed. The remainder of this section will discuss the scope and intent of this volume in its current form. The remainder of this paper will discuss how the papers in this Volume fit in with the current state of the theory of generalized inverses. Some reference will be made to recent work not covered by this volume. The referencing is not intended to be complete. The reader interested in further study of any of these topics is referred to the bibliographies of the cited papers. Cited papers which appear in this volume are denoted by double brackets.