Cravings often point to a deficiency in some particular nutrient, such as vitamin A, a vitamin that olives contain in abundance. Craving olives might also be a broader craving for savory foods in general.
Olives contain polyphenols, which have antibacterial, antioxidant and antifungal properties. Olives also stimulate the production of stomach acid to aid in digestion, boost the immune system, have a high protein-to-fat ratio and are supposed to smooth the skin. They are also a good source of monounsaturated fat and among the best natural sources of vitamin E.
While olives have a range of health benefits, eating too many could lead to an upset stomach or digestive problems, particularly when little else has been eaten. If you are looking for an alternative to olives, try meats, cheeses, fermented and soy-based foods or nutritional yeast.