Some people feel emotions when they look at abstract art. This article presents a ‘simulation’ theory that predicts which emotions they will experience, including those based on their aesthetic reactions. It also explains the mental processes underlying these emotions. This new theory embodies two precursors: an account of how mental models represent perceptions, descriptions, and self-reflections, and an account of the communicative nature of emotions, which distinguishes between basic emotions that can be experienced without knowledge of their objects or causes, and complex emotions that are founded on basic ones, but that include propositional contents. The resulting simulation theory predicts that abstract paintings can evoke the basic emotions of happiness, sadness, anger, and anxiety, and that they do so in several ways. In mimesis, models simulate the actions and gestures of people in emotional states, elicited from cues in the surface of paintings, and that in turn evoke basic emotions. Other basic emotions depend on synaesthesia, and both association and projection can yield complex emotions. Underlying viewers’ awareness of looking at a painting is a mental model of themselves in that relation with the painting. This self-reflective model has access to knowledge, enabling people to evaluate the work, and to experience an aesthetic emotion, such as awe or revulsion. The comments of artists and critics, and experimental results support the theory.