The history of the concept and the attempts for the realisation of a positron microprobe as well as the present state of development will be reviewed and evaluated. The principle and the design of a scanning positron microscope (SPM), built and operated at our university in Munich, will be presented. A pulsed positron beam, with a variable energy from 0.5 to 20 keV and a final spot diameter of currently 2 mum, can be electronically scanned over an area of 0.6 mm x 0.6 mm. In this way, microscopic regions of 2 mum x 2 mum x 0.1 mum can be evaluated. This beam is formed after a double-stage moderation of positrons emitted from a radioactive isotope acting as primary positron source. In the first stage, the beam spot of about 3 nun is reduced to a diameter of less than 20 mum. After the second moderation stage, this diameter is then further reduced to 2 mum. This is possible, due to the special properties of the magnetic lenses used in the design. In order to enable positron lifetime measurements, the positron beam is pulsed (time interval 20 ns). This feature makes this SPM the first and up to now only system worldwide. Included in the system is a conventional scanning electron microprobe for surface analysis and for the selection of interesting regions. Three-dimensional positron lifetime spectra of mechanically damaged and fatigued specimens will be presented. The real potential power of the SPM will be achieved when the intense reactor-based positron source at the new Munich research reactor FRM-II can be used, which will be possible now in the very near future.