Regular aerobic exercise improves memory and learning
In a study done at the University of British Columbia, researchers found that regular aerobic exercise, the kind that gets your heart and your sweat glands pumping, appears to boost the size of the hippocampus, the brain area involved in verbal memory and learning. Resistance training, balance and muscle toning exercises did not have the same results.
The finding comes at a critical time. Researchers say one new case of dementia is detected every four seconds globally. They estimate that by the year 2050, more than 115 million people will have dementia worldwide.
Working out reduces insulin resistance and inflammation
Exercise boosts your memory and thinking skills both directly and indirectly. It acts directly on the body by stimulating physiological changes such as reductions in insulin resistance and inflammation, along with encouraging production of growth factors — chemicals that affect the growth of new blood vessels in the brain, and even the abundance, survival, and overall health of new brain cells.
Exercise helps memory and thinking through both direct and indirect means. The benefits of exercise come directly from its ability to reduce insulin resistance, reduce inflammation, and stimulate the release of growth factors—chemicals in the brain that affect the health of brain cells, the growth of new blood vessels in the brain, and even the abundance and survival of new brain cells.
Exercise improves sleep and general mood
Indirectly, exercise improves mood and sleep, and reduces stress and anxiety. Problems in these areas frequently cause or contribute to cognitive impairment.
Based on studies conducted by the Johns Hopkins Center for Sleep, there's “solid evidence that exercise does, in fact, help you fall asleep more quickly and improves sleep quality.” 
While there’s only a little research done on linking exercise with mitigating insomnia, the available studies suggest that exercise indeed has an extraordinary impact on getting better sleep. 
One study shows that a single exercise session has a positive impact on a person suffering from chronic insomnia. This study found that even a moderate-intensity aerobic exercise like walking, running, cycling or swimming can make you fall asleep faster and give you a longer shut-eye. 
Studies have also found that aside from these two perks, making a habit out of working out has several benefits on the quality of your sleep – and it doesn’t really matter much whether you do it in the morning, midday or at night. 
Studies show people who exercise have stronger brain function responsible for thinking and memory
Many studies have suggested that the parts of the brain that control thinking and memory (the prefrontal cortex and medial temporal cortex) have greater volume in people who exercise versus people who don’t. “Even more exciting is the finding that engaging in a program of regular exercise of moderate intensity over six months or a year is associated with an increase in the volume of selected brain regions,” says Dr. Scott McGinnis, a neurologist at Brigham and Women’s Hospital and an instructor in neurology at Harvard Medical School.
Exercise and depression
Studies show that exercise can treat mild to moderate depression as effectively as antidepressant medication—but without the side-effects, of course. As one example, a recent study done by the Harvard T.H. Chan School of Public Health found that running for 15 minutes a day or walking for an hour reduces the risk of major depression by 26%. In addition to relieving depression symptoms, research also shows that maintaining an exercise schedule can prevent you from relapsing.
Exercise is a powerful depression fighter for several reasons. Most importantly, it promotes all kinds of changes in the brain, including neural growth, reduced inflammation, and new activity patterns that promote feelings of calm and well-being. It also releases endorphins, powerful chemicals in your brain that energize your spirits and make you feel good. Finally, exercise can also serve as a distraction, allowing you to find some quiet time to break out of the cycle of negative thoughts that feed depression.
Exercise and anxiety
Exercise is a natural and effective anti-anxiety treatment. It relieves tension and stress, boosts physical and mental energy, and enhances well-being through the release of endorphins. Anything that gets you moving can help, but you’ll get a bigger benefit if you pay attention instead of zoning out.
Try to notice the sensation of your feet hitting the ground, for example, or the rhythm of your breathing, or the feeling of the wind on your skin. By adding this mindfulness element—really focusing on your body and how it feels as you exercise—you’ll not only improve your physical condition faster, but you may also be able to interrupt the flow of constant worries running through your head.
Exercise and stress
Ever noticed how your body feels when you’re under stress? Your muscles may be tense, especially in your face, neck, and shoulders, leaving you with back or neck pain, or painful headaches. You may feel a tightness in your chest, a pounding pulse, or muscle cramps. You may also experience problems such as insomnia, heartburn, stomachache, diarrhea, or frequent urination. The worry and discomfort of all these physical symptoms can in turn lead to even more stress, creating a vicious cycle between your mind and body.
Exercising is an effective way to break this cycle. As well as releasing endorphins in the brain, physical activity helps to relax the muscles and relieve tension in the body. Since the body and mind are so closely linked, when your body feels better so, too, will your mind.
Exercise and ADHD
Exercising regularly is one of the easiest and most effective ways to reduce the symptoms of ADHD and improve concentration, motivation, memory, and mood. Physical activity immediately boosts the brain’s dopamine, norepinephrine, and serotonin levels—all of which affect focus and attention. In this way, exercise works in much the same way as ADHD medications such as Ritalin and Adderall.
Exercise and PTSD and trauma
Evidence suggests that by really focusing on your body and how it feels as you exercise, you can actually help your nervous system become “unstuck” and begin to move out of the immobilization stress response that characterizes PTSD or trauma. Instead of allowing your mind to wander, pay close attention to the physical sensations in your joints and muscles, even your insides as your body moves. Exercises that involve cross movement and that engage both arms and legs—such as walking (especially in sand), running, swimming, weight training, or dancing—are some of your best choices.
Outdoor activities like hiking, sailing, mountain biking, rock climbing, whitewater rafting, and skiing (downhill and cross-country) have also been shown to reduce the symptoms of PTSD.