We study nonparametric and regression estimators of treatment and spillover effects when interference is mediated by a network. Inference is nonstandard due to dependence induced by treatment spillovers and network-correlated effects. We derive restrictions on the network degree distribution under which the estimators are consistent and asymptotically normal and show they can be verified under a strategic model of network formation. We also construct consistent variance estimators robust to heteroskedasticity and network dependence. Our results allow for the estimation of spillover effects using data from only a single, possibly sampled, network.