Exponential random graph models (ERGMs) are a natural family of Gibbs measures on graphs, under which the presence of small subgraphs (e.g. triangles) may be encouraged or discouraged. The edges of an ERGM sample are not independent, especially at low temperatures where they exhibit a phase transition. Nevertheless, some markers of independence may be seen within metastable wells with respect to the Glauber dynamics. We will discuss some new results in this vein, namely central limit theorems for the edge count, vertex degree, and various subgraph counts. These results are quantitative, with bounds on the rate of convergence under the Wasserstein and Kolmogorov distances. Time permitting, we will discuss some ideas of the proof, which analyzes the evolution of certain relevant quantities under the Glauber dynamics.