'Inter-hemispheric inhibition' is used frequently to describe the action of one hemisphere in suppressing or impeding processing in its counterpart. It is widely believed that this is required in order to prevent a bilateral cerebrum giving rise to simultaneous and potentially competing outputs. It is argued here that a fundamental role of inter-hemispheric inhibition is to support contrast enhancing and integrative functions by co-opting the capacities of the two cerebral hemispheres. Drawing upon an extensive body of empirical data, derived largely from animal models, and associated theoretical modelling, it is demonstrated that inter-hemispheric projections act via mechanisms such as surround/lateral inhibition. The principal functional unit of callosal influence comprises a facilitatory centre and a depressing peripheral zone, which together shape the influence of converging inputs to pyramidal neurons. Inter-hemispheric inhibition is an instance of a more general feature of mammalian neural systems, whereby inhibitory interneurons act not simply to prevent over-excitation but to sculpt the output of specific circuits. The narrowing of the excitatory focus that occurs through crossed surround inhibition is a highly conserved motif of transcallosal interactions in mammalian sensory and motor cortices. A case is presented that the 'inter-hemispheric competition' model has been sustained, and its clinical derivatives promoted, by erroneous assumptions concerning that revealed by investigative techniques such as transcranial magnetic stimulation (TMS). The alternative perspective offered here is also shown to be consistent with known associations between the structural integrity of callosal projections and the magnitude of the motor deficits that are exhibited following stroke.