Interference is usually viewed as an obstacle to communication in wireless networks. In this talk, we describe a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea is that users should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise. Structured codes (such as lattices) ensure that these linear combinations can be decoded reliably, often at far higher rates than the messages individually. We demonstrate the potential of this scheme through examples drawn from cooperative communication including distributed MIMO and wireless network coding. Finally, we discuss connections to a new achievable scheme for the fast fading K-user interference channel which enables each user to achieve at least half its interference-free ergodic capacity. This is joint work with my advisor Michael Gastpar.