Studying and developing systems that can recognize, express, and “have” emotions is called affective computing. To create a Computational Models of Emotion (CMEs), one must first identify what kind of system to build, then find emotion theories that match its requirements. The relevant literature is vast. This survey is to help designers of CMEs that generate emotions—separated into emotion representation and elicitation—in computer agents and interfaces with this task. We give an overview of 67 CMEs from different domains, and identify which emotion theories they use and why. To better understand why CMEs use some theories, we also analyse instances where these CMEs use theories to express emotion. Lastly we summarize how CMEs generally use each theory. The survey is meant as a guideline for deciding which affective theories to use for new emotion-generating CME designs.