Here is a popular science article on intermittent fasting, something that extends life in mice, but which is not as well researched as calorie restriction, the gold standard for science on healthy life extension. There appears to be considerable overlap in the mechanisms involved in calorie restriction and intermittent fasting, but it's not all exactly the same when gene expression patterns are examined, to pick one example.
Many diet and exercise trends have origins in legitimate science, though the facts tend to get distorted by the time they achieve mainstream popularity. Benefits are exaggerated. Risks are downplayed. Science takes a backseat to marketing. One needn't look any further than the emerging trend of intermittent fasting for a prime example.
There is indeed a large body of research to support the health benefits of fasting, though most of it has been conducted on animals, not humans. Still, the results have been promising. Fasting has been shown to improve biomarkers of disease, reduce oxidative stress and preserve learning and memory functioning. [There] are several theories about why fasting provides physiological benefits. "The one that we've studied a lot, and designed experiments to test, is the hypothesis that during the fasting period, cells are under a mild stress. And they respond to the stress adaptively by enhancing their ability to cope with stress and, maybe, to resist disease."
But perhaps it isn't so much the fasting that produces health benefits, per se, as the resulting overall reduction in calorie intake (if, that is, you don't overeat on nonfasting days, which could create a caloric surplus instead of a deficit). That appears, at least, to be the case in slowing diseases such as cancer in mice. "Caloric restriction, undernutrition without malnutrition, is the only experimental approach consistently shown to prolong survival in animal models," In [a] study, mice fasted twice a week for 24 hours, but were otherwise permitted to eat at liberty. During nonfasting days, the mice overate. Overall, they did not lose weight, counteracting whatever benefits they might have seen from fasting. Intermittent fasting with compensatory overeating "did not improve mouse survival nor did it delay prostrate tumor growth," the study concluded.
Equally, there are studies showing that intermittent fasting without calorie restriction does extend life in nematode worms. A lot more research is needed to bring intermittent fasting up to the level of confidence that we can have in calorie restriction.