Emotion modeling has gained attention for almost two decades now due to the rapid growth of affective computing (AC). AC aims to detect and respond to the end-user's emotions by devices and computers. Despite the hard efforts being directed to emotion modeling with numerous tries to build different models of emotions, emotion modeling remains an art with a lack of consistency and clarity regarding the exact meaning of emotion modeling. This review deconstructs the vagueness of the term ‘emotion modeling' by discussing the various types and categories of emotion modeling, including computational models and its categories—emotion generation and emotion effects—and emotion representation models and its categories—categorical, dimensional, and componential models. This review deals with applications associated with each type of emotion model including artificial intelligence and robotics architecture, computer-human interaction applications of the computational models, and emotion classification and affect-aware applications such as video games and tutoring systems applications of emotion representation models.