Inferring and modeling the structure and dynamics of social networks is of critical importance for addressing a variety of challenging contemporary issues, ranging from global cooperation on climate change to control of infectious diseases. In this talk, I will discuss some of my recent work in developing new methods and approaches of statistical inference and stochastic modeling with applications to real-world problems such as homophily and behavior-disease interactions in social networks. I will first present my theoretical work concerning the evolution of homophily, an important trait that underlies the driving force for the formation of ties (structure) and cooperative interactions (function) in social networks. My approach combines coalescent theory in population genetics with evolutionary game theory, and allows inference of homophily for several phenotypes in a number of available datasets. I will then introduce voluntary vaccination behavior, a special form of human cooperation but central to public health interventions. In particular, I will discuss imitation behavior of vaccination in social networks and its impact on determining health outcomes. Finally I will present my most recent work on analyzing the concurrent spreading of vaccination behavior and seasonal influenza in an empirically observed social network. Integrating real data with behavior-disease models, this work, and the technical approach it introduces, unravels the role that social factors play in epidemiology and has practical implications for improving disease control efforts. Moreover, a model selection approach shows that the spread of vaccination behavior is driven jointly by social contagion and rational strategic responses to disease prevalence. The methodology has broad applicability to many other disparate, competitive spreading phenomena in social networks. This talk is based on joint work with Martin A. Nowak, James H. Fowler and Nicholas A. Christakis.