This chapter introduces trust modeling and trust management as a means of managing trust in digital systems. Transforming from a social concept of trust to a digital concept, trust modeling and management help in designing and implementing a trustworthy digital system, especially in emerging distributed systems. Furthermore, the authors hope that understanding the current challenges, solutions and their limitations of trust modeling and management will not only inform researchers of a better design for establishing a trustworthy system, but also assist in the understanding of the intricate concept of trust in a digital environment.