A new conceptual framework for understanding hemispheric specialization across evolution is proposed, and its multiple theoretical, clinical, and methodological implications are considered. According to the traditional understanding of hemispheric specialization, the “dominant” (usually left) hemisphere is in charge of language, whereas the “subdominant” (usually right) hemisphere is in charge of non-verbal, particularly visuo-spatial functions. While not incorrect, this understanding cannot be regarded as complete, since it does not permit any consideration of evolutionary continuities. Division of the brain into two hemispheres is not unique to humans ; it is a pervasive feature of the central nervous system throughout evolution. A number of morphological, cellular, and biochemical differences between the hemispheres exists, many of which are shared by multiple species. Therefore, it is only logical to assume that functional differences between the two hemispheres also exist and that they are invariant across multiple species. It is proposed that the fundamental functional difference between the two hemispheres is captured by the distinction between cognitive novelty and cognitive routines. According to this view, the left hemisphere is dominant in cognitive processing guided by previously formed, entrenched representations and strategies. In contrast, the right hemisphere is dominant for dealing with novel cognitive challenges, to which none of the previously formed routines or representations are readily applicable. The distinction between cognitive novelty and cognitive routines is universal and applicable to any organism capable of learning, unlike the verbal-nonverbal distinction which is applicable only to humans. Within this framework, language-mediated cognition is understood as a special case of cognition mediated by previously formed cognitive routines, verbal and non-verbal alike.