The allocation of collective benefits and costs represents a central challenge for individuals and organizations operating in uncertain environments, including interval and fuzzy data scenarios. Cooperative games under uncertainty provide a versatile game-theoretical framework and robust analytical tools to address these challenges, offering insights into decision-making and resource distribution. This survey reviews the current state of research in this emerging field, highlighting recent theoretical developments, methodological advances, and computational approaches. Furthermore, it examines how cooperative games under uncertainty extend classical cooperative game theory and discusses their practical applications and potential across economic decision-making, operations research, and strategic planning contexts. By synthesizing existing literature, this work aims to provide a comprehensive understanding of both the theoretical foundations and applied implications of these models, offering guidance for future research directions.