There is an idea called caloric restriction which has been demonstrated to increase lifespan in a number of model organisms. We don't know yet whether this also works in humans (it isn't an easy experiment to pull off). Some scientists are very convinced that it works.
2012, a study in monkeys suggested that it doesn't have an effect on aging. In 2014, a study in monkeys suggested that it does have an effect on aging. Both were published in very good journals (by the same publishing group, Nature)! I'd say that the jury is still out, but plenty of scientists would disagree, and I personally know several that are applying caloric restriction to their own diets.In