Networks have found a prominent place in our everyday life. In science, networks have been used to analyze interpersonal social relationships, communication, academic paper co-authorships and citations, protein interaction patterns, and much more. Popular books on networks and their analysis began to appear a decade ago, and online "networking communities" such as Facebook, MySpace, and LinkedIn now include millions of people from around the world. Formal statistical modeling for the analysis of network data has emerged as a major research topic in diverse areas of study. A Survey of Statistical Network Models aims to provide the reader with an entry point to the voluminous literature on statistical network modeling. It guides the reader through the development of key stochastic network models, touches upon a number of examples and commonalities across different parts of the network literature, and discusses major schools of thought in static and dynamic network modeling. In addition, it illuminates the interconnections between existing models. Despite the rich and extensive network modeling literature, many statistical questions remain unanswered. It is hoped that the concluding discussion of gaps and challenges will help the interested reader deduce important future research directions.