The words “organic farm” may not call to mind the South Bronx or Lower Manhattan. But the future of farming could well lie in dense urban centers, according to Columbia University's Dickson Despommier. (See "A New Direction in Agriculture: Up.") For the first time in history, the majority of human beings now live in cities. And with the world's expanding population facing a shortage of farmland, Despommier argues in a new book that the solution may lie in "vertical farms," or high-rise greenhouses that produce a city’s food while recycling its waste. No such farms exist, but the concept has sparked the imaginations of ecologists and architects alike. Here are ten designs envisioned for cities from New York to China.