  This paper provides a selective review of the statistical network analysis
literature focused on clustering and inference problems for stochastic
blockmodels and their variants. We survey asymptotic normality results for
stochastic blockmodels as a means of thematically linking classical statistical
concepts to contemporary research in network data analysis. Of note, multiple
different forms of asymptotically Gaussian behavior arise in stochastic
blockmodels and are useful for different purposes, pertaining to estimation and
testing, the characterization of cluster structure in community detection, and
understanding latent space geometry. This paper concludes with a discussion of
open problems and ongoing research activities addressing asymptotic normality
and its implications for statistical network modeling.
