The paper introduces a new strategy called "compute-and-forward" to harness interference in wireless networks to achieve higher rates between users. The key idea is that relays should decode linear functions of transmitted messages based on their observed channel coefficients rather than treating interference as noise. After decoding these linear equations, the relays send them to the destinations, which can recover their desired messages given enough equations. The underlying codes are based on nested lattices, ensuring that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to lattice points, and decoders recover equations of lattice points, which are then mapped back to equations over the finite field. This scheme is applicable even if transmitters lack channel state information. The paper develops a general framework for compute-and-forward in any relay network with linear channels and additive white Gaussian noise (AWGN), and compares it to classical relaying strategies in a distributed MIMO case study. The main results include achievable rates for sending equations over real and complex-valued channels, conditions for destinations to recover original messages, and extensions to successive cancellation and superposition coding.The paper introduces a new strategy called "compute-and-forward" to harness interference in wireless networks to achieve higher rates between users. The key idea is that relays should decode linear functions of transmitted messages based on their observed channel coefficients rather than treating interference as noise. After decoding these linear equations, the relays send them to the destinations, which can recover their desired messages given enough equations. The underlying codes are based on nested lattices, ensuring that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to lattice points, and decoders recover equations of lattice points, which are then mapped back to equations over the finite field. This scheme is applicable even if transmitters lack channel state information. The paper develops a general framework for compute-and-forward in any relay network with linear channels and additive white Gaussian noise (AWGN), and compares it to classical relaying strategies in a distributed MIMO case study. The main results include achievable rates for sending equations over real and complex-valued channels, conditions for destinations to recover original messages, and extensions to successive cancellation and superposition coding.