The fascinating idea that tools become extensions of our body appears in artistic, literary, philosophical, and scientific works alike. In the last 15 years, this idea has been reframed into several related hypotheses, one of which states that tool use extends the neural representation of the multisensory space immediately surrounding the hands (variously termed peripersonal space, peri-hand space, peri-cutaneous space, action space, or near space). This and related hypotheses have been tested extensively in the cognitive neurosciences, with evidence from molecular, neurophysiological, neuroimaging, neuropsychological, and behavioural fields. Here, I briefly review the evidence for and against the hypothesis that tool use extends a neural representation of the space surrounding the hand, concentrating on neurophysiological, neuropsychological, and behavioural evidence. I then provide a re-analysis of data from six published and one unpublished experiments using the crossmodal congruency task to test this hypothesis. While the re-analysis broadly confirms the previously reported finding that tool use does not literally extend peripersonal space, the overall effect sizes are small and statistical power is low. I conclude by questioning whether the crossmodal congruency task can indeed be used to test the hypothesis that tool use modifies peripersonal space.