How did ancient people store food before refrigeration?

Refrigeration is a pretty new phenomenon, so for millennia, people had to find clever ways to preserve food. These practices slowed the growth of microorganisms that could cause foodborne illnesses or lead food to rot. Many preservation practices other than refrigeration — like salting, drying, smoking, pickling and fermenting — have been used for a long time. 

These methods aside, how did ancient people store their leftovers?