The exponential random graph model has been a topic of continued research interest. The past few years especially has witnessed (exponentially) growing attention in exponential models and their variations. Emphasis has been made on the variational principle of the limiting normalization constant (free energy density), concentration of the limiting probability distribution, phase transitions, and asymptotic structures. This talk is based on joint work with several collaborators, including Sukhada Fadnavis (Harvard University), Richard Kenyon (Brown University), Charles Radin (University of Texas at Austin), and Alessandro Rinaldo (Carnegie Mellon University), and will focus on the phenomenon of phase transitions in (generalized) exponential random graphs.