When an object is tracked with the eyes, veridical perception of the motion of that object and other objects requires the brain to take account of and compensate for the eye movement. Here, I explore the effects of version and vergence eye movements on three-dimensional (3-D) motion perception. After demonstrating that eye movement compensation can be poor for detecting small objects moving in depth, I develop two models for how eye movement and visual signals may interact during the perception of 3-D motion direction. The first model assumes that the visual system is aiming to form an explicit representation of 3-D motion. From the results of a second experiment, on 3-D motion direction judgements, I show that this model could only hold with almost perfect 3-D motion compensation, contradicting the results from the first experiment. A second model assumes a much simpler strategy for estimating 3-D motion direction, based on recent experimental work. It predicts that compensation for vergence is not required because the Z-component of 3-D motion is not needed for direction judgements, consistent with the experimental results. This suggests that, for 3-D motion direction discrimination and angle judgements, extraretinal signals from vergence are not used.