This paper addresses the issue of risk from disasters occurring due to accidents in high-consequence technologies, e.g., nuclear and oil and gas. The focus is on the challenges posed to the representation and treatment of uncertainties in the assessment of such risk, given that the occurrence of such extreme disasters is extremely unlikely, and yet they occur. A general framework of analysis is proposed. (c) 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.