Detailed observation of the movement of individual animals offers the potential to understand spatial population processes as the ultimate consequence of individual behaviour, physiological constraints and fine-scale environmental influences. However, movement data from individuals are intrinsically stochastic and often subject to severe observation error. Linking such complex data to dynamical models of movement is a major challenge for animal ecology. Here, we review a statistical approach, state–space modelling, which involves changing how we analyse movement data and draw inferences about the behaviours that shape it. The statistical robustness and predictive ability of state–space models make them the most promising avenue towards a new type of movement ecology that fuses insights from the study of animal behaviour, biogeography and spatial population dynamics.