The Hanging Gardens of Babylon - one of the seven wonders of the ancient world - was a tiered series of sloped terraces richly decorated with trees, plants and grasses of every kind. It was located in Babylon, which is now in Iraq, about 90 km (55-ish miles) south of Baghdad. Nebuchadnezzar II (604-526 B.C.) is generally credited with building the garden as a gift to his wife, Amyitis, during the Neo-Babylonian Dynasty. Amyitis was from Medes and as such she was used to a lush and fertile land. She found the barren flat land of Babylon to be unwelcoming and downright depressing. (Given the pictures I've seen of Iraq, I'd have to agree). So Nebuchadnezzar had the gardens built to please her. (I could not find any information on whether or not this actually worked). Other archaeological findings suggest that they were actually built by Senaherib about a hundred years after the death of Nebuchadnezzar.
Regardless of when it was built, the gardens have been the inspiration for poetry and prose, and were written about in great detail by historian Diodorus Siculus, geographer Strabo and Philo of Byzantium (who first compiled the list of the seven wonders of the world). Philo writes that the plants were cultivated above ground and the roots of the trees are embedded in an upper terrace of the garden rather than in the earth. This raises the question of whether the Hanging Gardens were hydroponic or not. The irrigation which sustained the garden was brought in from the nearby Euphrates River and lifted via human-powered chain-pump (that's right, slaves were used to turn the wheels which kept the machine moving - synthetic energy sources being somewhat scarce in the fifth century B.C.) to the upper terraces and the water flowed down the sloping channels keeping the entire area moist. Whether soil was used at all (and evidence seems to suggest against it) or whether the garden was hydroponic remains an exercise for the archaeologist.
Some say that the Hanging Gardens never existed in the first place. This question arises from the fact that Herodotus never mentioned them. Herodotus gave a very descriptive account of Babylon, and described the Tower of Babel, among other features of the great city, but he never mentions the Gardens. There are no cuneiform tablets (what the ancient Babylonions used to write on) which mention any gardens, not to mention one which is reputed to be so impressive.
However, Robert Koldeway a German archaeologist found what is considered to be the cellar of the gardens, as many of the mechanisms described by Diodorus were found there. That and the fact that many of the accounts which mention the gardens state that only two structures in Babylon utilized stone in their construction - the Gardens and the north wall of the Northern Citadel - and stone was found in the walls of Koldeway's excavation. The north wall of the Northern Citadel had already been unearthed at the time.
I like to believe that they existed. But what do I know?