Positron re-emission microscopes (PRMs) are distinctly different from electron microscopes in the physical origin of their image contrasts. In a PRM, positrons of several keV energy are implanted into a sample and those positrons that are subsequently re-emitted at several eV are accelerated, focused and imaged. Contrast is produced by any process that affects the transport to, or re-emission from, the sample surface. After an introduction to the basic features of positron microscopy, applications of a PRM in four broad areas of research will be considered. These areas include: materials research, surface catalysis, microelectronic devices and biological systems.