Social capital is the value of the relationships we create and maintain within our social networks to gain access to and mobilize needed resources (e.g., jobs, moral support). Quantifying, and subsequently leveraging, social capital are challenging problems in the social sciences. Most work so far has focused on analyses from static surveys of limited numbers of participants. The explosion of online social media means that it is now possible to collect rich data about people's connections and interactions, in a completely ubiquitous, non-intrusive manner. Such dynamic social data opens the door to the more accurate measuring and tracking of social capital. Similarly, online data is replete with additional personal data, such as topics discussed in blogs or hobbies listed in personal profiles, that is difficult to obtain through standard surveys. Such information can be used to discover similarities, or implicit affinities, among individuals, which in turn leads to finer measures of social capital, including the often useful distinction between bonding and bridging social capital. In this work, we exploit these opportunities and propose a computational framework for quantifying and leveraging social capital in online communities. In addition to being dynamic and formalizing the notion of implicit affinities, our framework significantly extends current social network analysis research by modeling access and mobilization of resources, the essence of social capital. The main contributions of our framework include 1) hybrid networks that provide a way for potential and realized social capital to be distinguished; 2) the decoupling of bonding and bridging social capital, a formulation previously overlooked which coincides with empirical evidence; 3) the unification of multiple views on social capital, in particular, the seamless integration of resources. We demonstrate the broad applicability of our framework through a number of representative, real-world case studies to test relevant social science hypotheses. Assuming that the extraction of implicit affinities may be useful for community building, we built a large social network of blogs from an active, tech-oriented segment of the Blogosphere, using cross-references among blogs. We then used topic modeling techniques to extract an implicit affinity network based on the content of the blogs, and showed that potential sub-communities could be formed through increased bonding. A widespread assumption in sociology is that bonding is more likely than bridging in social networks. In other words, people are more likely to seek out others who are like them than attempt to link to those they share little or nothing with. We wanted to test that hypothesis, particularly in the context of online communities. Using Twitter, we created an experiment where hand-crafted accounts would tweet at regular intervals and use varied following strategies, including following only those with maximum affinity, following only those with no affinity, following random users, etc. Using the number of follow-backs as a surrogate for social capital, we showed that the assumed physical social behavior is also prevalent online, p < 0.01. There is much interest in computational social science to compare physical and cyber behaviors, test existing hypotheses on a large scale and design novel experiments. The advent of social media is also impacting public health, with growing evidence that some global health issues (e.g., H1N1 outbreak) may be discovered and tracked more efficiently by monitoring the content of social exchanges (e.g., blogs, tweets). In collaboration with colleagues from Health Sciences, we wanted to test whether broadly applicable health topics were discussed on Twitter, and to design and guide the process of discovering such themes. We gathered a large number of tweets over several regions of the United States over a one-month period, and analyzed their content using topic modeling techniques. We found that while clearly not a mainstream topic, health concerns were non-negligible on Twitter. By further focusing on tobacco, we discovered several subtopics related to tobacco (e.g., tobacco use promotion, addiction recovery), which indicate that analysis of the Twitter social network may help researchers better understand how Twitter promotes both positive and negative health behaviors. Finally, in collaboration with colleagues from Linguistics, we wanted to quantify the effect of social capital on second language acquisition in study abroad. Using questionnaire data collected from about 200 study abroad participants, we found that students participating in bridging relationships had significantly higher levels of language improvement than their counterparts, F(1,201) = 12.53, p < .0001.