This review examines brain and cognitive processes involved in arithmetic. I take a distinctly developmental perspective because neither the cognitive nor the brain processes involved in arithmetic can be adequately understood outside the framework of how developmental processes unfold. I review four basic neurocognitive processes involved in arithmetic, highlighting (1) the role of core dorsal parietal and ventral temporal-occipital cortex systems that form basic building blocks from which number form and quantity representations are constructed in the brain; (2) procedural and working memory systems anchored in the basal ganglia and frontoparietal circuits, which create short-term representations that allow manipulation of multiple discrete quantities over several seconds; (3) episodic and semantic memory systems anchored in the medial and lateral temporal cortex that play an important role in long-term memory formation and generalization beyond individual problem attributes; and (4) prefrontal cortex control processes that guide allocation of attention resources and retrieval of facts from memory in the service of goal-directed problem solving. Next I examine arithmetic in the developing brain, first focusing on studies comparing arithmetic in children and adults, and then on studies examining development in children during critical stages of skill acquisition. I highlight neurodevelopmental models that go beyond parietal cortex regions involved in number processing, and demonstrate that brain systems and circuits in the developing child brain are clearly not the same as those seen in more mature adult brains sculpted by years of learning. The implications of these findings for a more comprehensive view of the neural basis of arithmetic in both children and adults are discussed.