The pioneer works of Marc Dax and Paul Broca on the association between left hemisphere injuries and speech impairments, revealed one of the most intriguing properties of the brain – asymmetry. Since then, lateralized features have been observed in virtually all phylogenetic branches, suggesting evolutionary conservation, although its adaptive role is still not clear. In humans, the field remains greatly shaped by early observations on language, but the advent of brain imaging revealed that functional and structural laterality is not only widespread, extending to memory, decision-making and emotion, but also that it is plastic. In this review, we systematize information regarding structural and functional hemispheric asymmetries of the healthy brain and their associations with cognition and behavior. We briefly explore evolutionary theories and the pathways for asymmetry development, but mostly we focus on central nervous system asymmetries of the adult human, bridging towards the laboratory rodent for mechanistic explanations.