WORK IN PROGRESS
Aerobic fitness in children has been associated with faster cognitive processing speed and better executive control.  This correlation has been confirmed in school-aged children. In a randomized-control trial a daily exercise regimen enhanced school and reading performance in 36 children with reading difficulty, including some of which who had dyslexia. Students demonstrated improvements in reading accuracy, phonemic skill, verbal working memory and reduction in inattention symptoms as well as accelerated gains in standard school performance tests.  Additionally, there is evidence to suggest that regular exercise results in increased life expectancy over a sedentary lifestyle, even in individuals who had no pre-existing health factors such as heart disease normally attributed to a sedentary lifestyle. 
It was once believed that the adult brain was incapable of forming new neurons. However, it is now known that new neurons are created constantly (neurogenesis) in the hippocampus as well as other parts of the brain. Exercise has been found to stimulate this proliferation of nervous cells. Not only does physical activity increase neurogenesis, but also may increase baseline neuronal activity, allowing for these new neuronal cells to integrate into the existing neural structure.
Recently, neurotrophins have been shown to maintain the viability of neurons in adulthood and protect and restore neurons in response to injury and ageing. Neurotrophins regulate genetic expression required for synthesis of enzymes, structural proteins, or neurotransmitters responsible for affecting the morphology and function of brain neurons. When the function of these neurotrophins is blocked, animals have shown impairment in learning and memory. 
Brain-derived neutotrophic factor (BDNF), a growth factor which necessitates the survival of many types of neurons in the brain. Exercise facilitates the up-regulation of genes responsible for transcribing BDNF in certain brain areas, thus potentially making.  In an article published in Nature, the authors found a direct positive correlation between amount of physical activity in rats and transcription of the mRNA that codes for BDNF. . Most significantly, the authors found that BDNF was up-regulated the most in areas of the brain that have very high plasticity, indicating that BDNF plays a role in neuronal plasticity.
In addition to BDNF, exercise promotes the production of insulin-like growth factor (IGF-I) and basic fibroblast growth factor (bFGF) that support neuronal survival and differentiation in the developing brain and dendritic branching and synaptic machinery in the adult brain. 
 Exercise is brain food: The effects of physical activity on cognitive function
 Exercise and Brain Neutotrophins
 The Neurotrophin Hypothesis for Synaptic Plasticity
 Running increases cell proliferation and neurogenesis in the adult mouse dentate gyrus
 Aerobic Fitness and Neurocognitive Function in Health Preadolescent Children
 Follow-up of an exercise-based treatment for children with reading difficulties
 Physical Activity, Longevity, and All-Cause Mortality of College Alumni