Many environments in economics feature a cross-section of agents or units linked by a network of bilateral ties. I develop a framework to study dynamics in these cases. It consists of a vector autoregression in which innovations transmit cross-sectionally via bilateral links and which can accommodate general patterns of how network effects of higher order accumulate over time. In a first application, I take the supply chain network of the US economy as given and document how it drives the dynamics of sectoral prices. By estimating the time profile of network effects, the model allows me to go beyond steady state comparisons and study transition dynamics induced by granular shocks. As a result of different positions in the input-output network, sectors differ in both the strength and the timing of their impact on aggregates. In a second application, I discuss how to approximate cross-sectional processes by assuming that dynamics are driven by a network and in turn estimating the latter. The proposed framework offers a sparse, yet flexible and interpretable method for doing so, owing to networks` ability to summarize complex relations among units by relatively few non-zero bilateral links. Modelling industrial production growth across 44 countries, I obtain reductions in out-of-sample mean squared errors of up to 20% relative to a principal components factor model.