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This chapter is from the forthcoming The Oxford Handbook of Affective Computing edited by Rafael Calvo, Sidney K. D'Mello, Jonathan Gratch, and Arvid Kappas. This chapter discusses appraisal theory, the most influential theory of emotion in affective computing today, including how appraisal theory arose, some of its well-known variants, and why appraisal theory plays such a prominent role in computational models of emotion. The authors describe the component model framework, a useful framework for organizing and contrasting alternative computational models of emotion and outline some of the contemporary computational approaches based on appraisal theory and the practical systems they help support. Finally, the authors discuss open challenges and future directions.