Many elite athletes go high up in the mountains to do some altitude training as hypoxia (reduced oxygen pressure in the air) may give some physiological gains on top of normal training at the sea level. They still do that even if science does not really support these ideas. Some say believing is everything, but it is likely that good training camp in a good terrain where you can devote all your efforts just to training and recovering explains most of the fitness gains due to high altitude training period.
However, hypoxia or altitude training may atually be more beneficial for us “normal”people, who are not training like elite athletes. Recent evidence to support these ideas comes from a study by Camacho-Cardenosa et al. who recently showed that high-intensity interval training under normobaric intermittent hypoxia for 12 weeks in overweight/obese women seems to be promising for reducing body fat content with a concomitant increase in muscle mass.
We have also already some two years ago reviewed the acute responses of exercise and hypoxia in a human body, and health benefits of living and being and training in altitude. Acute responses are summarized in the figure below, but check out also this table for studies showing health benefits in health and disease.