Despite a lack of scientific consensus on the definition of emotions, they are generally considered to involve several modifications in the mind, body, and behavior. Although psychology theories emphasized multi-componential characteristics of emotions, little is known about the nature and neural architecture of such components in the brain. We used a multivariate data-driven approach to decompose a wide range of emotions into functional core processes and identify their neural organization. Twenty participants watched 40 emotional clips and rated 119 emotional moments in terms of 32 component features defined by a previously validated componential model. Results show how different emotions emerge from coordinated activity across a set of brain networks coding for component processes associated with valuation appraisal, hedonic experience, novelty, goal-relevance, approach/avoidance tendencies, and social concerns. Our study goes beyond previous research that focused on categorical or dimensional emotions, by highlighting how novel methodology combined with theory-driven modeling may provide new foundations for emotion neuroscience and unveil the functional architecture of human affective experiences.