My research interest has been in understanding the human communities formed through interpersonal social activities. Participation in online communities on social network sites such as Twitter has been observed to influence people's behavior in diverse ways including financial decision-making and political choices, suggesting the rich potential for diverse applications ranging from information search, organization, to organizational study and reform. My work focuses on computational problems relating to extracting and tracking active communities from large-scale, dynamic, and context-rich social data. First, how can one discover communities from online social actions? I introduce "mutual awareness" and "transitive awareness" to discover communities from online users' actions. Extensive experiments on real-world blog datasets show that an efficient algorithm based on these ideas discovers communities with excellent results. Second, how can one extract sustained evolving communities? I present "FacetNet", the first generative framework, to extract communities with sustained membership and to analyze their evolutions in a unified process. The experiments suggest that by incorporating historic membership into discovering new communities, FacetNet's results are more accurate, more robust to noise than prior methods. Third, how can one extract communities with rich contexts? I present "MetaFac", the first graph-based tensor factorization framework for analyzing the dynamics of rich-context social networks. Metafac consists of a novel relational hypergraph representation for modeling social data of arbitrarily many dimensions or relations and an efficient factorization method for community extraction on a given metagraph. It can discover community evolution along multiple dimensions, and the extracted community structures can be employed to predict users' potential interests on media objects such as news stories. The prediction results significantly outperform the baseline methods by an order of magnitude, suggesting the utility of leveraging rich-context with community analysis to inform future decision-making. Finally, I present two applications that leverage community analysis into understanding patterns of users' activities. "COLACT" discovers multi-relational structures from social media streams. "ContexTour" efficiently tracks the community evolution, smoothly adapts to the community changes, and visualizes the community activities in various dimensions through a novel "contextual contour map". [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]