While relatively little is known about the psychology of domestic pigs, what is known suggests that pigs are cognitively complex and share many traits with animals whom we consider intelligent. This paper reviews the scientific evidence for cognitive complexity in domestic pigs and, when appropriate, compares this literature with similar findings in other animals, focusing on some of the more compelling and cutting-edge research results. The goals of this paper are to: 1) frame pig cognition and psychology in a basic comparative context independent of the livestock production and management setting; and 2) identify areas of research with pigs that are particularly compelling and in need of further investigation. We summarize and discuss several areas of comparative psychology, including nonsocial and social cognition, self-awareness, emotion, and personality. We conclude that there are several areas of research in which the findings are suggestive of complex psychology in pigs. We conclude by calling for more noninvasive cognitive and behavioral research with domestic pigs in non-laboratory settings that allow them to express their natural abilities.