Good cognitive abilities (CA) enable autonomy, improve social inclusion and act preventively. Regular physical activity (PA) reduces the risk of developing Alzheimer’s disease (AD) and, at the same time, it reduces the decline of CA and stimulates neurogenesis. So PA in connection with cognitive training, nutrition and social interaction has a positive effect on general CA and the central nervous system, the central executor, memory and attention, and reduces the likelihood of developing dementia. Our objective was to examine which sort and intensity of PA is preferred. We did a review, restricted only to human studies, of transparent scientific articles and sample surveys carried out and published in the period between 2001 and 2016 based on the keywords: age, aging, physical activity, physical abilities, cognitive abilities, memory and Alzheimer’s disease. According to results CA and PA interact, as an increasing PA of only 10% reduces the risk of dementia and AD significantly. However, there is a question of appropriate intensity of exercise. Low-intensity aerobic exercise has a positive effect on the visual spatial perception and attention, whereas moderate PA has a positive impact on general CA, working memory and attention, verbal memory and attention and vice versa. While the majority of experts recommends vigorous or moderate exercise, many of them warn that higher intensity requires more attention to PA and less to cognitive processes, particularly in terms of reducing reactions, selective attention and flexibility to tasks. There is also a further question what PA should be like. Although some experts believe that the best combination is aerobic PA and exercises against resistance, it is not entirely clear whether the improvement in CA is a result of cardiac vascular fitness. On the other hand, for most elderly it is more suitable to perform an alternative form (not anaerobic) of PA due to comorbidity and actual fragility. We can conclude that PA has a positive effect on CA, but an appropriate intensity and the type of exercise remain unsolved. For the relevant findings it is absolutely necessary to have an interdisciplinary approach.