The production of a positron microbeam using the high-brightness beam developed at Brandeis University and possible applications of this microbeam to spatially resolved defect studies and positron microscopy are reviewed. The high-brightness beam consists of a W(110) primary moderator and two remoderation stages which provide a 500-fold increase in brightness. With this brightness increase and microbeam optics, the authors are able to form a 12 mu m FWHM beam (48 mrad pencil half-angle) at 5 keV beam energy. The well characterised small-diameter beam is particularly adaptable for determining defect concentration and structure, both laterally and in a depth-profiling mode. In the case of a transmission positron microscope or a positron reemission microscope operating in a high-magnification mode, efficient image formation requires the use of a microbeam to maximise the number of positrons in the area being imaged. Results of the scanning microbeam tests and the application of a microbeam to positron microscopy and defect studies are reviewed.