Smartphone and tablet proliferation is generating an enormous increase in the demand for multimedia content. Modern wireless networks cannot support this demand and its large projected growth. We explain how caching of popular content can play a fundamental role in addressing this problem and how several novel mathematical and algorithmic problems arise. 

We focus on the Femtocaching problem and the Coded Caching problem introduced by Maddah-Ali and Niesen and discuss how caching is very promising for giving gains that scale surprisingly well in the size of the wireless system. Unfortunately, we show that for these gains to appear, the cached files must be separated in a number of blocks that scales exponentially in the number of users and files. We show how this can problem can be resolved if we modify the Maddah-Ali and Niesen scheme to place and deliver coded packets in a less optimistic way.