Existing models of laterality, while often successful at describing circumscribed domains, have not been successful as explanations of the overall patterns of hemispheric asymmetries. It is therefore suggested that a new approach is needed based on shared contributions to adaptive hemispheric roles rather than functional and structural intrahemispheric similarities. This paper proposes a model of laterality, the Janus model, based on evolutionary considerations of complementary hemispheric roles. It is proposed that the left hemisphere has the role of anticipating future scenarios and choosing between them while the right hemisphere has the role of integrating ongoing information into a unitary view of the past in order to immediately detect and respond to novel and unexpected events. Evidence for these complementary roles is provided in research on motor control and semantic priming. Finally, the Janus model is contrasted with efforts to cast the frequency model as a general model of laterality.