A number of scientific endeavors of national and international interest involve populations with interacting and/or interfering units. In these problems, measurements about interactions and interference (e.g., social structure and familial relations) are available, in addition to traditional measurements about unit-level outcomes and covariates. Formal statistical models for the analysis of this type of data have emerged as a major topic of interest in diverse areas of science. In this talk, I will review a few ideas and open research problems that are central to this burgeoning literature, placing emphasis on inference and other core statistical issues. Then I will turn to describe: (1) a new notion of non-ignorability that applies to network sampling designs, (2) an inference strategy that can be used to obtain valid estimates in these settings, and (3) a strategy to extend the Rubin framework for estimating causal effects in the presence of social interference. This is joint work with Don Rubin.