It is particularly appropriate for this Journal to devote one of its issues to the subject of the scanning transmission electron microscope (STEM) and its uses because the initial stimulus for its invention was precisely the problem of discerning ultrastructural details in biological material. To a large extent the capabilities of the instrument have been shown to offer the potential of solving many such problems and what is most needed today is to put such instruments in the hands of biologists together with the information on how and when to use them. This issue should go a long way in satisfying this latter need. The purpose of this article is to try to provide a setting for the more detailed expositions which follow. In order to do this we must necessarily give a very general treatment and avoid detail. In addition, we will concentrate on those aspects of the STEM which apply to biological uses, and we will therefore ignore the more esoteric applications, such as convergent beam diffraction patterns.