Social network analysis is the study of the pattern of relationships between a collection of actors. Although the tendency is to look at friendship networks between individuals, this restriction is not necessary. In this informal talk/discussion, I will present an introduction to the basic concepts in social network analysis and then review some of the more popular models that researchers have developed which all have the exponential family form. The challenge for researchers lies in trying to specify a model for which parameters can be estimated; Markov Chain Monte Carlo methods have become an essential part of this process.