The success of the human species in interacting with the environment depends on the ability to maintain spatial stability despite the continuous changes in sensory and motor inputs owing to movements of eyes, head and body. In this paper, I will review recent advances in the understanding of how the brain deals with the dynamic flow of sensory and motor information in order to maintain spatial constancy of movement goals. The first part summarizes studies in the saccadic system, showing that spatial constancy is governed by a dynamic feed-forward process, by gaze-centred remapping of target representations in anticipation of and across eye movements. The subsequent sections relate to other oculomotor behaviour, such as eye -head gaze shifts, smooth pursuit and vergence eye movements, and their implications for feed-forward mechanisms for spatial constancy. Work that studied the geometric complexities in spatial constancy and saccadic guidance across head and body movements, distinguishing between self-generated and passively induced motion, indicates that both feed-forward and sensory feedback processing play a role in spatial updating of movement goals. The paper ends with a discussion of the behavioural mechanisms of spatial constancy for arm motor control and their physiological implications for the brain. Taken together, the emerging picture is that the brain computes an evolving representation of three-dimensional action space, whose internal metric is updated in a nonlinear way, by optimally integrating noisy and ambiguous afferent and efferent signals.