Quantitative risk assessment may never become a rigorous scientific discipline because of the inherent difficulties in working with highly uncertain and often controversial data and methods, and because the predictions of risk assessment may not be subject to validation in their most important areas of application. However, the potential benefits of having quantitative estimates of risk may make quantitative risk assessment a valuable adjunct to traditional methods for making individual and social decisions about health hazards in the home, workplace, and general environment. Risk assessment, which is the process of estimating risks to populations exposed to hazardous agents or activities, must be distinguished from risk management, which is the process of forming and implementing a strategy for accepting or abating the risks. To the extent possible, these two processes should be kept separate. Quantitative risk assessment is in principle capable of estimating individual or lifetime excesses of specific health effects from exposures to a specified hazard. These excesses may be estimated on an absolute basis or expressed as a relative risk in comparison with the baseline risk that would exist without exposure. An individual risk is usually expressed in terms of the probability of developing the health effect in some time period following a specified exposure, whereas a population risk is the overall number of effects expected in a defined population with a defined distribution of exposure levels and patterns. The variation of risk with time after exposure may imply a constant absolute risk, a constant relative risk, or some other dependence on time, usually after a minimal latent period has elapsed. Risk estimates can rarely be made directly from observed human data, and models for extrapolating or projecting risk estimates from the conditions of observation to the actual conditions of exposure must be used. Dose-response relationships are used for extrapolating from high laboratory or occupational exposures to low exposures encountered more frequently in human populations. Thresholds of dose or nonlinear dose-response relationships may be related to nonlinear pharmacokinetics prior to the ultimate exposure of the critical organ to the proximate carcinogen or other hazardous agent. Time-response models estimate risks for periods after exposure longer than have been observed in epidemiologic studies. Extrapolations from experiments with laboratory animals to humans are made difficult because of great differences in size, lifespan, physiology, and metabolism between human and animal.(ABSTRACT TRUNCATED AT 400 WORDS)