This study examines the state of the art in research on risk/disaster operations management in supply chains (SCs) and closed loop SCs (CLSCs) from a viability perspective. In addition, it integrates key research elements that could act as enablers of more efficient evolution paths in SC/CLSC management. To this end, the existing literature is categorized according to the nature of the disruptive event (risk or disaster), the event formulation, the structure of SC network (SC/CLSC), the source of the disruptive event, the decision‐making level (strategic, tactical or operational), the aim of risk/disaster management (viability–sustainability) and the relevant treatment methods. The target of this literature taxonomy process is threefold: (a) literature analysis with respect to risk and disaster management in SCs; (b) the formulation of a framework for selecting the most suitable treatment policies to manage risk/disaster events at strategic, tactical and operational levels, with the aim of achieving transition to viable SC networks; and (c) the codification of a methodological approach when developing models for achieving viability. The latter is introduced by proposing a dynamic model as an exemplary model to explain the state evolution of an SC network governed by dynamics subjected to viability constraints and, also, to reveal regulatory feedback mechanisms to achieve desired states.