Among the best-known facts of the brain are the contralateral visual, auditory, sensational, and motor mappings in the forebrain. How and why did these evolve? The few theories to this question provide functional answers, such as better networks for visuomotor control. However, these theories contradict the data, as discussed here. Instead we propose that a 90-deg turn on the left side evolved in a common ancestor of all vertebrates. Compensatory migrations of the tissues during development restore body symmetry. Eyes, nostrils and forebrain compensate in the direction of the turn, whereas more caudal structures migrate in the opposite direction. As a result of these opposite migrations the forebrain becomes crossed and inverted with respect to the rest of the nervous system. We show that such compensatory migratory movements can indeed be observed in the zebrafish (Danio rerio) and the chick (Gallus gallus). With a model we show how the axial twist hypothesis predicts that an optic chiasm should develop on the ventral side of the brain, whereas the olfactory tract should be uncrossed. In addition, the hypothesis explains the decussation of the trochlear nerve, why olfaction is non-crossed, why the cerebellar hemispheres represent the ipsilateral bodyside, why in sharks the forebrain halves each represent the ipsilateral eye, why the heart and other inner organs are asymmetric in the body. Due to the poor fossil record, the possible evolutionary scenarios remain speculative. Molecular evidence does support the hypothesis. The findings may shed new insight on the problematic structure of the forebrain.