We study communication in networks with multiple source-destination pairs and relays. In such networks, the channel output at any destination receiver consists of both the desired signal and interference. In this setting the relay can help forward the desired message of a user to the destination receiver, or help forward interference to a receiver to improve its ability to cancel the interference. Focusing on the impact of interference forwarding, we define a new relay-interferer channel (RIC) model, which serves as the basic building block for the study of interference in multiuser networks. Using the RIC we show that correlation between the codebooks of the relay and the interferer (e.g. superposition codebooks) is essential for obtaining performance benefits from interference forwarding. We conclude that in order to achieve rate gains from relaying interference using the decode-and-forward strategy, a superposition codebook is required. Otherwise, this relay strategy has the same rate as interference cancellation at the receiver. We also conclude that compress-and-forward is not useful for forwarding interference and has no better performance than just treating interference as noise at the decoder.