Despite the tremendous progress in the estimation of generative models, the development of tools for diagnosing their failures and assessing their performance has advanced at a much slower pace. Very recent developments have investigated metrics that quantify which parts of the true distribution is well modeled, and, on the contrary, what the model fails to capture, akin to precision and recall in information retrieval. In this paper we present a general evaluation framework for generative models that measures the trade-off between precision and recall using R\'enyi divergences. Our framework provides a novel perspective on existing techniques and extends them to more general domains. As a key advantage, it allows for efficient algorithms that are directly applicable to continuous distributions directly without discretization. We further showcase the proposed techniques on a set of image synthesis models.