Digital platforms generate unprecedented traces of human behaviour, offering new methodological approaches to understanding collective action, polarisation, and social dynamics. Through analysis of millions of digital traces across multiple studies, we demonstrate how online behaviours predict offline action: Brexit-related tribal discourse responds to real-world events, machine learning models achieve 80% accuracy in predicting real-world protest attendance from digital signals, and social validation through "likes" emerges as a key driver of mobilization. Extending this approach to conspiracy narratives reveals how digital traces illuminate psychological mechanisms of belief and community formation. Longitudinal analysis of YouTube conspiracy content demonstrates how narratives systematically address existential, epistemic, and social needs, while examination of alt-tech platforms shows how emotions of anger, contempt, and disgust correlate with violence-legitimating discourse, with significant differences between narratives associated with offline violence versus peaceful communities. This work establishes digital traces as both methodological innovation and theoretical lens, demonstrating that computational social science can illuminate fundamental questions about polarisation, mobilisation, and collective behaviour across contexts from electoral politics to conspiracy communities.