Low-beta fusion research in open-ended magnetic geometries (mirrors) is reviewed. This material, extracted from the report of a USAEC panel convened to examine mirror research, has been edited and revised to include recent information. It is intended to present an overview of the achievements, methods and rationale of this area of fusion research. Topics covered include the scope of mirror research, classical end losses, and fusion economics, minimum-B stabilization of flute instability, theoretical and experimental results concerning loss-cone instabilities, and a summary of experiments and experimental techniques.