Trust relationships occur naturally in many diverse contexts such as collaborative systems, e-commerce, interpersonal interactions, social networks, and semantic sensor web. As agents providing content and services become increasingly removed from the agents that consume them, the issue of robust trust inference and update becomes critical. There is a need to find online substitutes for traditional (direct or face-to-face) cues to derive measures of trust, and create efficient and robust systems for managing trust in order to support decision-making. Unfortunately, there is neither a universal notion of trust that is applicable to all domains nor a clear explication of its semantics or computation in many situations. We motivate the trust problem, explain the relevant concepts, summarize research in modeling trust and gleaning trustworthiness, and discuss challenges confronting us. The goal is to provide a comprehensive broad overview of the trust landscape, with the nitty-gritties of a handful of approaches. We also provide details of the theoretical underpinnings and comparative analysis of Bayesian approaches to binary and multi-level trust, to automatically determine trustworthiness in a variety of reputation systems including those used in sensor networks, e-commerce, and collaborative environments. Ultimately, we need to develop expressive trust networks that can be assigned objective semantics.