Translation of an observer through a static environment generates a pattern of optical flow that specifies the direction of self-motion, but the retinal flow pattern is confounded by pursuit eye movements. How does the visual system decompose the translational and rotational components of flow to determine heading? It is shown that observers can perceive their direction of self-motion during stationary fixations and pursuit eye movements and with displays that simulate the optical effects of eye movements. Results indicate that the visual system can perform the decomposition with both continuous and discontinuous fields on the basis of flow-field information alone but requires a three-dimensional environmental structure to do so. The findings are inconsistent with general computational models and theories based on the maximum of divergence, oculomotor signals, or multiple fixations but are consistent with the theory of reliance on differential motion produced by environmental variation in depth.