Cities have been built upwards rather than outwards for the last 150+ years, so it makes perfect sense to use the same practices for growing food. That is exactly what “Vertical farming” hopes to achieve. There are a couple of advantages in doing this other than the obvious space saving factor. Food can be grown in modern facilities which are automated to allow control over light, humidity and temperature giving crops optimal growing conditions 24 hours a day, similar to a regular greenhouse. Old high rise buildings could also be reused for this purpose rather than demolishing them.
The term vertical farming is not new as it was first coined by Gilbert Ellis Bailey in 1915. Back then the technology didn't exist to make this a fileable venture but with current innovations at hand this technique could well become widely used helping to supply food to a growing population.