The occurrence of large-scale crises is a great challenge for people. In such cases, many levels of public life are affected and recovery takes time and considerable resources. Therefore, approaches and tools for predicting and preventing crises, as well as models and methods for crisis management and crisis overcoming, are necessary. In this review, we present approaches, models, and methods that support decision-making in relation to the prevention and resolution of large-scale crises. We divide crises into three types: natural disasters, pandemics, and economic crises. For each type of crisis situation, the types of applied tasks that are solved and the corresponding models and methods that are used to support decision-makers in overcoming the crises are discussed. Conclusions are drawn on the state of the art in this area and some directions for future work are outlined.