... were ancient Greeks and Romans eating?

Scene from a butchery of Ancient Athens. The butcher is cutting a cow’s leg. On the right, his assistant. In the background, another piece of meat hangs from a vine-arbour.

Meat
They did not have turkeys (these were imported from America) but they most certainly had chicken of various kinds, such as the ones of Chalkida, Tanagra or Rhodes. The Rhodes’ chickens would be very meaty but did not produce many eggs. The Ancient Greeks also ate, as we do, plenty of pork and goat’s meat but no big animals, such as cows which were used for farming. The poorer people ate cow’s meat usually during the great sacrifices of public religious celebrations. Also, there was a separate donkey meat market in Athens.
They also usually ate game. Wild boar, deer and birds were in the menu of richer people who also had the time to go hunting. They ate snails, too. It was also very usual (as it is actually today, in the country) for them to eat boiled meat which lasted longer. They would also though roast, char-grill or cook meat in a pot, known as "gastra". They also cooked it in various sauces with ingredients such as oil, salt, pepper, vinegar, dill, mint, thyme, cumin, oregano, fennel etc.

Dairy products
Milk was a very usual dish accompaniment. Cheese, in great variety, was not just a usual "meze" but also an ingredient for delicious recipes. They made "tyrotarachos" (cheese and salted fish), "mytotos" (cheese, garlic pieces, oil, honey), "kykeonas" (cheese, barley flour, wine, thyme, herbs) and cheese rolls or pies (shredded cheese, flour, honey).

Cereal
The Ancient Greeks cooked wheat in several ways: after peeling it in a mortar they boiled it in water and then served it with milk it which made it look whiter. They also cooked it without passing it through a mill, a recipe from Chios. This was wheat that they soaked in water for about ten days (changing that water regularly), then it was melted, they threw away its peel and they sun-dried the rest of it. It was with this material that they made bread and desserts.
They also made all kinds of "poltos" (pulp made of flour, water, spices), "ptisani" (barley flour) and "chondros" (wheat grain). Flour was prepared in wooden or stone mortars and in domestic mills and it was then sieved. In several places, such as the islands, they mainly used barley. A tradition which carries on until contemporary Greece is the "healthy" barley bread from Lemnos and Crete, which is sold in super-markets.

Breads
They made several types of bread, which varied according to the ingredients ("maza" when from barley and "artos" when from wheat) or the existence of any pre-baking ("zymitis", "azymos") and the type of baking ("apopyrias", "epnitis", "sponditis"). The baker’s profession can be traced back to the beginning of the 2nd century B.C

Vegetables
Cabbage, cauliflower, leeks, lettuce, marrows, cucumbers, stalks carrots, radishes, bulbs, onions, celery, nettle, cress, and artichokes. Garlic was eaten by rowers as it was considered to be particularly nutritious. Also, broad beans or flour made from broad beans was used for bread, lentils, beans, peas and yellow peas. Olives and olive oil, were very popular, the latter always used in cooking pots to make them non-stick. Certain areas were particularly famous for the local olive oil, such as Attika, Samos, Sikyona (Kiato), Evoia, Fokida, Crete and Cyprus.

Fruit
There were forty-four varieties of fig, thirty-two varieties of apples and six varieties of pears. Also, plums, quince, pomegranates, bitter oranges and possibly oranges and lemons. Grapes were eaten either fresh or dried and were also used for making wine while the boiled new wine was also used in baking cakes. Jujubes, carobs and dried fruit were also part of the Ancient Greeks’ diet.

Scene from and ancient fish market. The old the white-haired fish-mongrel is cutting a large fish, possibly a tuna fish. The bald and bearded customer is leaning against his cane and he’s either giving his order or bargaining about the price.

Seafood
Many varieties of fish were mainly eaten salted ("tarichi"). The area of Kyzikos in Asia Minor was famous for the export of processed tuna. Ieron, the Syracuse tyrant is known to have sent to Egypt one thousand barrels of salted fish, in the end of the 3rd century BC.
The Ancient Greeks ate plenty of seafood just like Modern Greeks, such as "trichides" (sardines), "melanouros", "lavrakas", "trigli" (red mullet), "sparos", "echinous" (sea-urchins), "kochyli", "astakos", "karides" (prawns), "sipies" (cuttlefish). These were either boiled, or roasted or fried.

Wines
They were produced generally in the same way as they are today. What was different was the way they were stored as they did not use wooden barrels or bottles but amphoras. They produced all kinds of wine but they would drink it "watered", that is two parts of water for one part of wine.
Retsina which is an ancient wine of Attika, was probably made by mistake! They used to spread "retsini" (resin) on amphoras to make them water-tight and the wine would then acquire the taste of "retsini", hence the "retsina" wine. (Many centuries later, a certain mistake in the transportation seems to have triggered the discovery of champagne!!).
To improve the taste of wine, they also added seawater, chalk and several herbs. The most well known wines were made in Mendi of Chalkidiki, Naxos of Sicily, Thassos and Rhodes