Epidemiologic methods can be categorized into demographic studies of mortality and morbidity and observational studies that are either retrospective or prospective. Some of the limitations of demographic studies are illustrated by a review of one specific mortality study showing possible relationship of nuclear fallout to leukemia. Problems of accuracy of diagnosis or causes of death on death certificates, estimates of population, migration from areas of study, and the issue of "ecological fallacy" are discussed. Retrospective studies have such problems as recall of previous environmental exposure, selection bias and survivor bias. In environmental epidemiology, prospective studies have been used. The problems associated with these studies are illustrated by reviewing some of the details of the study of effects of microwave radiation on embassy employees in Moscow. The study population had to be reconstructed, individuals had to be located and information on exposure status had to be obtained by questionnaire. The relatively small size of the exposed group permitted the detection of only fairly large relative risks. Despite these limitations, epidemiologic studies have been remarkably productive in elucidating etiological factors. They are necessary since "the proper study of man is man."