Where are my hands? The brain can answer this question using sensory information arising from vision, proprioception, or touch. Other sources of information about the position of our hands can be derived from multisensory interactions (or potential interactions) with our close environment, such as when we grasp or avoid objects. The pioneering study of multisensory representations of peripersonal space was published in Behavioural Brain Research almost 30 years ago [Rizzolatti G, Scandolara C, Matelli M, Gentilucci M. Afferent properties of periarcuate neurons in macaque monkeys. II. Visual responses. Behav Brain Res 1981;2:147-63]. More recently, neurophysiological, neuroimaging, neuropsychological, and behavioural studies have contributed a wealth of evidence concerning hand-centred representations of objects in peripersonal space. This evidence is examined here in detail. In particular, we focus on the use of artificial dummy hands as powerful instruments to manipulate the brain's representation of hand position, peripersonal space, and of hand ownership. We also review recent studies of the 'rubber hand illusion' and related phenomena, such as the visual capture of touch, and the recalibration of hand position sense, and discuss their findings in the light of research on peripersonal space. Finally, we propose a simple model that situates the 'rubber hand illusion' in the neurophysiological framework of multisensory hand-centred representations of space.