Calorie restriction with optimal nutrition involves reducing the level of calories in the diet by up to 40% or so while still maintaining sufficient intake of micronutrients. This has been shown to slow aging and extend maximum life span in most species tested to date, with most mammal studies having used mice and rats. In primate studies while calorie restriction is definitely shown to significantly improve health and reduce incidence of age-related disease, the evidence isn't so good for meaningful extension of life span.
Why would calorie restriction reliably extend life span in short lived species but not in longer-lived species? The current thinking is that this response evolved because it allows individuals better odds of surviving seasonal famines, such that they can procreate later. When you are a mouse a seasonal famine is a large fraction of a life span, but this is not the case for humans, so it makes sense to see greater plasticity of life span in response to environmental circumstances in mice. There is selection pressure for this outcome in a short-lived species that isn't present for a long-lived species.
This researcher has a different take on the origin of the calorie restriction response, in which extension of life span is not the effect being selected for. Instead enhanced longevity is a side-effect of the actual selected trait, which is greater cellular recycling and repair that enables the ability to better reproduce when food is scarce. This still leaves the open question of why life extension is large in short-lived animals but not in humans, given that the short-term measures of the effects of calorie restriction on metabolism are remarkably similar between mice and humans.
Scientists have known for decades that severely restricted food intake reduces the incidence of diseases of old age, such as cancer, and increases lifespan. This effect has been demonstrated in laboratories around the world, in species ranging from yeast to flies to mice. There is also some evidence that it occurs in primates. The most widely accepted theory is that this effect evolved to improve survival during times of famine. "But we think that lifespan extension from dietary restriction is more likely to be a laboratory artefact."
Lifespan extension is unlikely to occur in the wild, because dietary restriction compromises the immune system's ability to fight off disease and reduces the muscle strength necessary to flee a predator. "Unlike in the benign conditions of the lab, most animals in the wild are killed young by parasites or predators. Since dietary restriction appears to extend lifespan in the lab by reducing old-age diseases, it is unlikely to have the same effect on wild animals, which generally don't live long enough to be affected by cancer and other late-life pathologies."
Dietary restriction, however, also leads to increased rates of cellular recycling and repair mechanisms in the body. [The] new theory is that this effect evolved to help animals continue to reproduce when food is scarce; they require less food to survive because stored nutrients in the cells can be recycled and reused. It is this effect that could account for the increased lifespan of laboratory animals on very low nutrient diets, because increased cellular recycling reduces deterioration and the risk of cancer.