Hemispheric asymmetries play an important role in almost all cognitive functions. Despite this tremendous relevance, our understanding of the neurobiological fundaments of lateralization is just in its infancy. In the last decade I tried to streamline my research on bird and human asymmetries such that overlapping phenomena were studied with diverse neuroscientific methods in both model systems from neuron to behavior. What is now lacking is an overarching theory that integrates the findings from diverse model systems. Such a theory has to outline the unfolding of lateralized neural activity patterns at three steps of analysis: 1) Asymmetries of encoding, where left-right differences of feature detectors of early sensory processing stages enable asymmetrical categorical identification; 2) Asymmetrical activation of early cortical areas that result in a spread of activity in associated cortical networks; 3) Lateralized action generation where only one hemisphere gains transient, but complete control of our reactions.