Environmental epidemiology and health risk and impact assessment have long grappled with problems of uncertainty in data and their relationships. These uncertainties have become more challenging because of the complex, systemic nature of many of the risks. A clear framework defining and quantifying uncertainty is needed. Three dimensions characterise uncertainty: its nature, its location and its level. In terms of its nature, uncertainty can be both intrinsic and extrinsic. The former reflects the effects of complexity, sparseness and nonlinearity; the latter arises through inadequacies in available observational data, measurement methods, sampling regimes and models. Uncertainty occurs in three locations: conceptualizing the problem, analysis and communicating the results. Most attention has been devoted to characterising and quantifying the analysis--a wide range of statistical methods has been developed to estimate analytical uncertainties and model their propagation through the analysis. In complex systemic risks, larger uncertainties may be associated with conceptualization of the problem and communication of the analytical results, both of which depend on the perspective and viewpoint of the observer. These imply using more participatory approaches to investigation, and more qualitative measures of uncertainty, not only to define uncertainty more inclusively and completely, but also to help those involved better understand the nature of the uncertainties and their practical implications.