Squirrels are predominantly herbivourous, subsisting on seeds and nuts, but many will eat insects and even small vertebrates.
FOOD & HORDING
Squirrels are forest dwellers and they primarily eat nuts and seeds, but will also eat berries, fungus and insects.
Squirrels horde food in small amounts in several locations when it's abundant. Some caches of seeds are never recovered and instead become seedlings.
Even among tree squirrels, the species matters as to the primary food source and storage strategy. Pine squirrels (Tamiasciurus), like Douglas and American red squirrels, are larder hoarders who eat primarily tree seeds (pine cones); as well as other foods that they can find such as mushrooms, buds, catkins, flowers and berries, storing all of their food in a single location or midden (larder).
Eastern gray squirrels and fox squirrels, on the other hand, prefer tree mast like acorns, walnuts, pecans; as well as fruit, berries, and seeds. These squirrels are scatter hoarders, burying each nut its own hiding place. These species have adapted quite well to foods available in an urban setting and are highly opportunistic feeders - eating atypical foods when necessity and opportunity are present.