The tragic attacks of September 11 and the bioterrorist threats with respect to anthrax that followed have raised a set of issues regarding how we deal with events where there is considerable ambiguity and uncertainty about the likelihood of their occurrence and their potential consequences. This paper discusses how one can link the tools of risk assessment and our knowledge of risk perception to develop risk management options for dealing with extreme events. In particular, it suggests ways that the members of the Society for Risk Analysis can apply their expertise and talent to the risks associated with terrorism and discusses the changing roles of the public and private sectors in dealing with extreme events.