Attempts by various regulatory authorities to perform risk assessments on substances such as Environmental Tobacco smoke (ETS) have been controversial and fraught with error. An understanding of Risk Assessment methodology is therefore useful. Public health risk assessment is a discipline which uses toxicological data derived from animal studies and human epidemiology, combined with information about the degree of exposure, to predict quantitatively the likelihood that a particular adverse response will be seen in a specific human population. Risk assessment is a process whereby the magnitude of a specific risk is characterized so that decision makers can conclude whether the potential hazard is sufficiently great that it needs to be managed or regulated. This approach has been employed since the 1980's to assess whether the broad array of environmental risks are significant or trivial, for example in establishing acceptable daily intakes (ADI) for pesticide residues in food, setting drinking water standards etc... The risk assessment paradigm consists of four subdisciplines, (1) hazard identification, (2) dose-response assessment, (3) exposure assessment, and (4) risk characterization. Hazard identification involves determining whether exposure to an agent could, at any dose, cause an adverse health effect. Dose-response evaluations define the relationship between the dose of the agent and the probability of a specific adverse effect, typically derived from animal studies. Exposure assessment quantifies the uptake of the agent from the environment by oral, inhalation and dermal routes of exposure. Risk characterization summarizes and interprets the collated data, identifying the limitations and uncertainties in the risk estimates. To demonstrate the practical application of the risk assessment paradigm, the methodology employed to assess the (public) health risk from dioxin emissions for residents in the nearby vicinity of a Municipal Waste Incinerator is presented and the difficulties of applying such a model to ETS is discussed.