The present review is devoted to discussion of the principal stages of development of mirror electron microscopy. In the mirror electron microscope (MEM) the electron beam is reflected in a retarding electric field near the sample surface, and as a result the object being studied is not subjected to bombardment by the probe particles. This permits information to be obtained on the geometrical relief of the surface and the microfields in it. The review discussses the problems of MEM design, the different modes of operation, and questions of the limiting resolution. The theory of contrast formation for the geometrical relief and also for electric and magnetic microfields is discussed in detail. Experimental data are presented on investigation of a broad class of objects--semiconductors, dielectrics, and magnetic structures--in MEM. Various techniques for quantitative measurement of static and dynamic microfields on the surface of solid samples are described.