Why do the left and right sides of the brain have different functions? Having a lateralized brain, in which each hemisphere processes sensory inputs differently and carries out different functions, is common in vertebrates, and it has now been reported for invertebrates too. Experiments with several animal species have shown that having a lateralized brain can enhance the capacity to perform two tasks at the same time. Thus, the different specializations of the left and right sides of the brain seem to increase brain efficiency. Other advantages may involve control of action that, in Bilateria, may be confounded by separate and independent sensory processing and motor outputs on the left and right sides. Also, the opportunity for increased perceptual training associated with preferential use of only one sensory or motoric organ may result in a time advantage for the dominant side. Although brain efficiency of individuals can be achieved without the need for alignment of lateralization in the population, lateral biases (such as preferences in the use of a laterally-placed eye) usually occur at the population level, with most individuals showing a similar direction of bias. Why is this the case? Not only humans, but also most non-human animals, show a similar pattern of population bias (i.e., directional asymmetry). For instance, in several vertebrate species (from fish to mammals) most individuals react faster when a predator approaches from their left side, although some individuals (a minority usually ranging from 10 to 35%) escape faster from predators arriving from their right side. Invoking individual efficiency (lateralization may increase fitness), evolutionary chance or simply genetic inheritance cannot explain this widespread pattern. Using mathematical theory of games, it has been argued that the population structure of lateralization (with either antisymmetry or directional asymmetry) may result from the type of interactions asymmetric organisms face with each other.