This paper compares lateralized behaviour in invertebrates and vertebrates and considers whether any similar patterns indicate homology or are examples of convergent evolution. It covers evidence for left-right asymmetries of memory consolidation, approach and withdrawal in social, predatory and predation situations, aggressive behaviour and sexual behaviour. Although the pattern of these asymmetries in the brains of vertebrate species is the mirror image of the pattern in invertebrates, the direction of behavioural asymmetry matches since sensory inputs cross the midline in vertebrates (for vision) but not in invertebrates (for olfaction and vision). Similarities in the lateralization pattern in vertebrate and invertebrate species suggest that a basic plan of lateralized brain function may have been conserved during the transition from invertebrates to vertebrates.