Appraisal theories of emotion have proposed detailed—and causal—hypotheses about the connection between situations and emotional responding, and between the components that constitute emotional responding. Many of these hypotheses present computational challenges to scientific research, in that they require the analysis of numerous mental and bodily changes simultaneously over time. In this thesis, I applied statistical models of machine learning to address these challenges, and to investigate hypotheses concerning interaction effects, curvilinear associations, feedback among emotion components, synchronization of components, and the felt experience of synchronized changes (e.g., feeling angry). Results of the four studies generally supported the algorithmic complexity that underlies emotion unfolding, and that modelling these complexities is necessary to differentiate patterns of emotional responding quantitatively and qualitatively. Using a novel measure for emotional synchronization, I showed experimentally that changes in motivation, physiology, and expression responses synchronized following a manipulation of the appraised importance of a situation.