This survey describes recent progress in the field of Affective Computing (AC), with a focus on affect detection. Although many AC researchers have traditionally attempted to remain agnostic to the different emotion theories proposed by psychologists, the affective technologies being developed are rife with theoretical assumptions that impact their effectiveness. Hence, an informed and integrated examination of emotion theories from multiple areas will need to become part of computing practice if truly effective real-world systems are to be achieved. This survey discusses theoretical perspectives that view emotions as expressions, embodiments, outcomes of cognitive appraisal, social constructs, products of neural circuitry, and psychological interpretations of basic feelings. It provides meta-analyses on existing reviews of affect detection systems that focus on traditional affect detection modalities like physiology, face, and voice, and also reviews emerging research on more novel channels such as text, body language, and complex multimodal systems. This survey explicitly explores the multidisciplinary foundation that underlies all AC applications by describing how AC researchers have incorporated psychological theories of emotion and how these theories affect research questions, methods, results, and their interpretations. In this way, models and methods can be compared, and emerging insights from various disciplines can be more expertly integrated.