Our understanding of the neural basis of human cognition and its relation to behaviour is limited by the extent to which we can observe its underlying components. Neural activity elicited by a given stimulus can be decomposed in parallel threads of cognitive computation, each specialising on a different aspect of the stimulus. Conventional methods are fundamentally limited to tease apart these components within the stimulus-specific brain activity, therefore obscuring our understanding of the underlying mechanisms. I will build a framework to distil these threads by modelling their (trial-by-trial) distinct spatiotemporal trajectories and the interaction between them. Furthermore, I propose that the way our brains process stimuli, and in particular how these different components organise and relate to each other, can be critical to characterise subjects at the psychological and clinical level. However, it is unclear how to relate these complex models of stimulus processing to the subject phenotypes. I will develop principled algorithms to automatically discover which specific aspects of the modelled brain activity are most relevant to the traits under study. In summary, this multidisciplinary project brings together modelling and prediction across different data modalities to offer a novel temporal analytic account of how different threads of brain activity give rise to cognition, and how the nature of these elements relates to population variability. I will tackle three important questions that are representative of the addressed methodological challenges: in the study of decision-making, the relation between value representation, decision-formation and attention; in sleep research, which specific aspects of the sleep cycle are most altered in insomniacs; in the field of pain perception, the disambiguation of nociception and salience, and how these diverge in chronic pain. Despite diverse, these questions are conceptually linked by ideas presented here.