Armies in foreign territory, if well-funded and planned, would have a supply train with foodstuffs and a variety of merchants, prostitutes, and stragglers in tow. If there was not a lot of food, or the food ran out, or the soldiers were undisciplined, they would forage, potentially razing the area in the process.

Longer trips through neutral or allied territory usually involved a reciprocal arrangement where food would either be provided, or licenses to purchase from local/regional merchants would be honored. (This last one in particular played a huge part in negotiations with the original crusading armies, who were allowed to purchase from Greek merchants or not depending on the whims and political goals of the Basileus and the overall rowdiness of the armies camped outside Constantinople.) Navy logistics could also play a part in coastal campaigns or sieges with unfettered access to water (e.g. Nicaea).

Then there's the strategic element to supply by both providing food and passage as a gesture of goodwill or denying access to foraging to hamper an army's progress. Both of these were also major factors in the Crusades.

On a lesser note, there's also eating your own horses (Crusade armies during several sieges, blood-drinking amongst Mongol and Turkic cavalry), and eating your own men or the bodies of the dead enemy (al-Qalanisi and al-Athir talk a bit about the original Crusaders doing this due to provisions being so low, but how much of this is polemical I have no idea).