A myriad of social media services are emerging in recent years that allow people to communicate and express themselves conveniently and easily. The pervasive use of social media generates massive data at an unprecedented rate. It becomes increasingly difficult for online users to find relevant information or, in other words, exacerbates the information overload problem. Meanwhile, users in social media can be both passive content consumers and active content producers, causing the quality of user-generated content can vary dramatically from excellence to abuse or spam, which results in a problem of information credibility. Trust, providing evidence about with whom users can trust to share information and from whom users can accept information without additional verification, plays a crucial role in helping online users collect relevant and reliable information. It has been proven to be an effective way to mitigate information overload and credibility problems and has attracted increasing attention.

As the conceptual counterpart of trust, distrust could be as important as trust and its value has been widely recognized by social sciences in the physical world. However, little attention is paid on distrust in social media. Social media differs from the physical world - (1) its data is passively observed, large-scale, incomplete, noisy and embedded with rich heterogeneous sources; and (2) distrust is generally unavailable in social media. These unique properties of social media present novel challenges for computing distrust in social media: (1) passively observed social media data does not provide necessary information social scientists use to understand distrust, how can I understand distrust in social media? (2) distrust is usually invisible in social media, how can I make invisible distrust visible by leveraging unique properties of social media data? and (3) little is known about distrust and its role in social media applications, how can distrust help make difference in social media applications?

The chief objective of this dissertation is to figure out solutions to these challenges via innovative research and novel methods. In particular, computational tasks are designed to {\it understand distrust}, a innovative task, i.e., {\it predicting distrust} is proposed with novel frameworks to make invisible distrust visible, and principled approaches are develop to {\it apply distrust} in social media applications. Since distrust is a special type of negative links, I demonstrate the generalization of properties and algorithms of distrust to negative links, i.e., {\it generalizing findings of distrust}, which greatly expands the boundaries of research of distrust and largely broadens its applications in social media.