Empirical-Bayes methods offer potentially dramatic improvements in statistical accuracy over conventional statistical methods. We provide an elementary introduction to empirical-Bayes analysis of occupational and environmental hazard surveillance data. Such analyses are especially well suited to situations in which many associations must be examined, but few or none can be estimated precisely. Statistical issues in hazard surveillance are reviewed, followed by a discussion of the rationale and methods for empirical-Bayes analyses, using a study of occupational exposures and cancer mortality to illustrate key concepts. Finally, the assumptions underlying empirical-Bayes analyses are discussed critically, with special attention to the "exchangeability" assumptions that distinguish empirical-Bayes from conventional methods.