We survey the recent, fast-growing literature on peer effects in networks. An important recurring theme is that the causal identification of peer effects depends on the structure of the network itself. In the absence of correlated effects, the reflection problem is generally solved by network interactions even in non-linear, heterogeneous models. By contrast, microfoundations are generally not identified. We discuss and assess the various approaches developed by economists to account for correlated effects and network endogeneity in particular. We classify these approaches in four broad categories: random peers, random shocks, structural endogeneity and panel data. We review an emerging literature relaxing the assumption that the network is perfectly known. Throughout, we provide a critical reading of the existing literature and identify important gaps and directions for future research.