The methods used for risk assessment from exposure to chemicals are well established. in most cases where toxicity other than carcinogenesis is being considered, the standard method relies on establishing the No Observed Adverse Effect Level (NOAEL) in the most sensitive animal toxicity study and using an appropriate safety factor (SF) to determine the exposure which would be associated with an acceptable risk. For carcinogens a different approach is used because it has been argued there is no threshold of effect. Thus mathematical equations are used to extrapolate from the high doses used in ani-mal experiments. These methods have been strongly criticised in recent years on several grounds. The most cogent criticisms are a) the equations are not based on a thorough understanding of the mechanisms of carcinogenesis and b) the outcome of a risk assessment based on such models varies more as a consequence of changes to the assumptions and equation used than it does from the data derived from carcinogenicity experiments. Other criticisms include the absence of any measure of the variance on the risk assessment and the selection of default values that are very conservative. Recent advances in the application of risk assessment emphasise that measures of both the exposure and the hazard should be considered as a distribution of values. The outcome of such a risk assessment provides an estimate of the distribution of the risks.