The recent interest in analyzing the network structure of complex systems has fueled a large body of research on both models of network structure and algorithms to automatically discover patterns for use in predictive models. However, robust statistical models, which can accurately represent distributions over graph populations, and sample efficiently from those distributions, are critical to assess the evaluate the performance of analytic algorithms and the significance of discovered patterns. However, unlike metric spaces, the space of graphs exhibits a combinatorial structure that poses significant theoretical and practical challenges to accurate estimation and efficient sampling/inference. In this talk, I will discuss our recent work on modeling distributions of networks, both attributed and unattributed, and outline how the methods can be used for inference and evaluation.