Affective computing encompasses the research and development of systems that can recognize, express, and “have” emotions. Its literature is already vast, which is a hindrance for newcomers. Those who wish to create Computational Models of Emotion (CMEs) must first identify what kind of system they want to build, then identify affective theories that match its requirements. This survey aims to help designers of CMEs that generate emotions in computer agents and user interfaces with this latter task. We give an overview of 63 CMEs from different domains, and identify which affective theories they use and why. Some of these CMEs also use affective theories to express emotion and for other design purposes. We also analyse these instances to better understand the complete system. The survey closes with a brief summary of how CMEs generally use each encountered theory. The survey is meant as a guideline for deciding which affective theories to use for new CME designs that generate emotions.