Dynamics of social processes in populations, such as the spread of emotions, influence, opinions, and mass movements (often referred to individually and collectively as contagions), are increasingly studied because of their economic, social, and political impacts. Moreover, multiple contagions may interact and hence studying their simultaneous evolution is important. Within the context of social media, large datasets involving many tens of millions of people are leading to new insights into human behavior, and these datasets continue to grow in size. Through social media, contagions can readily cross national boundaries, as evidenced by the 2011 Arab Spring. These and other observations guide our work. Our goal is to study contagion processes at scale with an approach that permits intricate descriptions of interactions among members of a population. Our contributions are a modeling environment to perform these computations and a set of approaches to predict contagion spread size and to block the spread of contagions. Since we represent populations as networks, we also provide insights into network structure effects, and present and analyze a new model of contagion dynamics that represents a person's behavior in repeatedly joining and withdrawing from collective action. We study variants of problems for different classes of social contagions, including those known as simple and complex contagions.