1. Characterizing the spatiotemporal variation of animal behaviour can elucidate the way individuals interact with their environment and allocate energy. Increasing sophistication of tracking technologies paired with novel analytical approaches allows the characterisation of movement dynamics even when an individual is not directly observable. 2. In this study, high-resolution movement data collected via global positioning system (GPS) tracking in three dimensions were paired with topographical information and used in a Bayesian state-space model to describe the flight modes of migrating golden eagles (Aquila chrysaetos) in eastern North America. 3. Our model identified five functional behavioural states, two of which were previously undescribed variations on thermal soaring. The other states comprised gliding, perching and orographic soaring. States were discriminated by movement features in the horizontal (step length and turning angle) and vertical (change in altitude) planes, and by the association with ridgelines promoting wind deflection. Tracked eagles spent 2%, 31%, 38%, 9% and 20% of their day time in directed thermal soaring, gliding, convoluted thermal soaring, perching and orographic soaring, respectively. The analysis of the relative occurrence of these flight modes highlighted yearly, seasonal, age, individual and sex differences in flight strategy and performance. Particularly, less energy-efficient orographic soaring was more frequent in autumn, when thermals were less available. Adult birds were also better at optimising energy efficiency than sub-adults. 4. Our approach represents the first example of a state-space model for bird flight mode using altitude data in conjunction with horizontal locations, and is applicable to other flying organisms where similar data are available. The ability to describe animal movements in a three-dimensional habitat is critical to advance our understanding of the functional processes driving animals’ decisions.