  We study the role of caches in wireless interference networks. We focus on
content caching and delivery across a Gaussian interference network, where both
transmitters and receivers are equipped with caches. We provide a
constant-factor approximation of the system's degrees of freedom (DoF), for
arbitrary number of transmitters, number of receivers, content library size,
receiver cache size, and transmitter cache size (as long as the transmitters
combined can store the entire content library among them). We demonstrate
approximate optimality with respect to information-theoretic bounds that do not
impose any restrictions on the caching and delivery strategies. Our
characterization reveals three key insights. First, the approximate DoF is
achieved using a strategy that separates the physical and network layers. This
separation architecture is thus approximately optimal. Second, we show that
increasing transmitter cache memory beyond what is needed to exactly store the
entire library between all transmitters does not provide more than a
constant-factor benefit to the DoF. A consequence is that transmit zero-forcing
is not needed for approximate optimality. Third, we derive an interesting
trade-off between the receiver memory and the number of transmitters needed for
approximately maximal performance. In particular, if each receiver can store a
constant fraction of the content library, then only a constant number of
transmitters are needed. Our solution to the caching problem requires
formulating and solving a new communication problem, the symmetric multiple
multicast X-channel, for which we provide an exact DoF characterization.
