Before revision: See manuscript for full abstract .
After revision: I study identification, estimation and inference for spillover effects in experiments where units' outcomes may depend on the treatment assignments of other units within a group. I show that the commonly-used linear-in-means regression identifies a weighted sum of spillover effects with some negative weights, and characterize the estimand that is recovered by a simple difference in means in the presence of spillovers. My results reveal the potential pitfalls of failing to flexibly account for spillover effects in policy evaluation. I then propose nonparametric estimators that overcome these issues and are consistent and asymptotically normal under a precise relationship between the number of parameters of interest, the total sample size and the treatment assignment mechanism. I show that these results can be used to rank assignment mechanisms for experimental design. These findings are illustrated using data from a conditional cash transfer program and with simulations .