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The article begins with an account of prewar German work, particularly that of von Ardenne, who established the theoretical basis of a scanning electron microscope and constructed an instrument which was primarily intended to overcome chromatic aberration when relatively thick specimens were examined by transmission. Neither this microscope nor a different one built a few years later in the U. S. A. attained sufficient resolution to gain acceptance and the reasons for this are examined. The remainder of the article deals with work carried out in the Cambridge University Engineering Department over the years from 1948 to about 1965, when the first successful commercial instrument was produced. The contributions made by successive research students are explained, as are also the nonscientific factors which influenced the course of the development.