In coevolutionary networks, the network topology evolves in feedback with dynamical processes on the network nodes. Nodes have state variables that react to the network topology, and the network topology in turn reacts to the nodal state variables. Oftentimes there is a timescale separation, which simplifies the analysis of such systems. A more complicated setting is where the change in network topology occurs at a comparable time scale to nodal dynamics. This talk presents an overview of recent selected work on coevolutionary models with an emphasis on network formation in the following settings: (i) dynamic flow of benefits and costs, (ii) transient link establishment costs, and (iii) latent preferential attachment.