This talk will first explain a bit about exponential-family random graph models (ERGMs) for networks: What they are, their history, and challenges in fitting them using maximum likelihood estimation. Ordinarily, MLE is considered a gold standard of frequentist statistical estimation, partly because it has favorable asymptotic properties. Yet in the case of ERGMs for networks, the very idea of a consistent estimator is tricky to define: Letting the number of nodes tend to infinity, using a fixed data-generating parameter, can itself be problematic. The talk will present some published work on ideas that ameliorate this problem as well as some intriguing recent empirical results.