The Romans were very efficient in feeding their armies, but did it differently than most.
They had three nodes, or 'bases', in their logistical train. Roman Governers were required to raise the food in their jurisdictions, the 'Supply Base' for the army and then the food would be transported to the 'Operational Base'. The Operational Base was a fort, port, city, camp, a node near the armies' operations but not actually on the battlefield.
These Operational Bases would link the supplies with the 'Tactical Base'; a camp. Example: In the movie Gladiator in the first scene Maximus is off fighting a battle while the Emperor is back at a camp a short bit away.
This would be where the legionnaires would rest and recharge for the day. The Romans were robust in their logistics.
Xerxes and Darius used joint ground-naval invasions to keep food moving on the water. This is why river-ways were so important. Herodotus claims that Xerxes' army drained entire rivers and his beasts drained entire lakes.
"From these regions he passed by the cities of the mainland, one of which has near it a lake of about thirty stadia in circuit, full of fish and very salty; this was drained dry by watering the beasts of burden alone."
"But the Greeks who received Xerxes' army and entertained the king himself were brought to such a degree of misery, that they were driven from house and home. Witness the case of the Thasians, who received and feasted Xerxes' army on behalf of their towns on the mainland; Antipatrus son of Orgeus, as notable a man as any of his townsmen, chosen by them for this task, rendered them an account of four hundred silver talents expended on the dinner."
EDIT/Added: Forgot to mention, Herodotus also claims that Xerxes sent ships far ahead of his armies to create 'food dumps' that would be awaiting the arrival of his troops; setting up a food supply before they even got there.
Less specific, but other armies like the Huns, Mongols, Vikings, would pillage and forage from where they conquered. Sun Tzu wrote, "Bring with you from home, but forage on the enemy." This was much more common than the robust system of the Romans and the coordinated exhaustion of resources by Xerxes' "Million Man Army".
Mongols also rode what they ate, feeding off of their horses if there were no other food sources.
A reply to /u/bliss0
Closer to 1700, soldiers during the 80YW and 30YW (1550s to 1650s) were notoriously brutal, partly due to the inability of their erstwhile state employers to provide for them, thus they tend to "help themselves" so to speak and ransack the place where they are located or billeted.
Here I spoke a bit about how this came to play in the military revolution. Here I spoke on how difficult it was to get funding in the first place, let along send them to the right place. And here I spoke of the infamous Sack of Antwerp, where soldiers whose pay was in arrears for years mutinied.
Soldiers became infamous for their cruelty and methods of exacting loot and payment, and in German lexicon they still ring to today.
Logistics was a major issue even for victors of great battles. The Swedish army had to continue to insist that her allies pay and provide for the upkeep of the Swedish army, lest they ransack the states of her own allies!
There are occasional lights of brilliance in logistics, however. Wallenstein the greatest military contractor of all time set up a state-across states with a sophisticated taxation and tribute system to prevent looting. The Army of Flanders was periodically supplied with fresh troops up the Spanish Road, and in most cases the daily bread was something they could rely on.