This paper is a literature review of research on the compressive response of fiber-reinforced composite materials. The review is organized by subject and the papers are included in one of three main sections; (1) Compression Test Methods, (2) Failure Theories and Failure Mechanisms, and (3) Experimental Investigations. The compression test method section includes a discussion of 15 compression test methods. The section on failure theories and failure mechanisms discusses failure theories and observations including those dealing with fiber microbuckling, transverse tension failure, and fiber kink-band formation. The section on experimental investigations summarizes data that is available in the literature. Tables are presented that list information on the evaluation of test methods and summarize experimentally developed data. These tables provide an index for quick reference to the research discussed in this paper.