The exponential random graph is arguably the most popular model for the statistical analysis of network data. However despite its widespread use, it is very complicated to handle from a statistical perspective, mainly because the likelihood function is intractable for all but trivially small networks. This talk will outline some recent work in this area to overcome this intractability. In particular, we will outline some approaches to carry out Bayesian parameter estimation and show how this can be extended to estimate Bayes factors between competing models.