We review statistical exponential family models that recognize the complex dependencies within relational data structures. Such models are being used to modeling the contact network that underlies infectious disease transmission. These models make it possible to represent key structural parameters of real networks, and then use these parameters to simulate disease spread across a dynamic network with the observed structural features. In this talk we review model inference from complete and sampled network data. To represent a dynamic network, both the structural regularities in the network and the dynamics of partnership formation and dissolution must be addressed. We demonstrate such a network model and apply the method to HIV spread in sub-Saharan Africa.