Managing the societal risks from extreme events requires making informed decisions. Decisions are in relation to the desired values of probabilities associated with possible consequences, what are unacceptable consequences (including defining their type and duration), and who might be exposed to risks. Different dimensions of risk including probabilities, consequences, and its source have been discussed in the literature. Such dimensions shape decisions about risk. However, in addition to the technical aspects, ultimately managing risk requires socially negotiated rules. This chapter describes how technical risk analysis can be integrated with public values. The chapter starts with a broad definition of risk and defines its different dimensions. Then the chapter defines guidelines for principled compromises in managing societal risks of extreme events. The chapter also defines the roles and scope in this complex process of risk analysis, risk communication, and risk perception. The proposed guidelines can support decision-makers in making more informed and more transparent decisions about safety, sustainability, and resilience.