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This study discerns the relationship between discrete emotions and their underlying components from a detailed dataset of continuous annotations of more than 50 emotion variables during short films. Appraisal theories predict that discrete emotions arise from a combination of components. Specifically, the Component Process Model (CPM) highlights the prime role of appraisal following motivation, expression, physiology and feeling. We include annotations from all these domains and reveal a hierarchical organisation of discrete emotions by appraisal of valence and self-relevance. Furthermore, we apply predictive models to understand the contribution of emotion components to discrete emotions. We find that all 13 discrete emotions in our dataset can be significantly predicted as a function of emotion components. Our study contributes key insights using machine learning to the longstanding question of what is an emotion and underscores the centrality of appraisal in the generation of emotion. This has important implications on the complexity and function of emotion as an adaptive process.