This monograph aims to provide an overview of the Dark Web landscape, suggest a systematic, computational approach to understanding the problems, and illustrate with selected techniques, methods, and case studies developed by the University of Arizona AI Lab Dark Web team members. This work aims to provide an interdisciplinary and understandable monograph about Dark Web research along three dimensions: methodological issues in Dark Web research; database and computational techniques to support information collection and data mining; and legal, social, privacy, and data confidentiality challenges and approaches.  It will bring useful knowledge to scientists, security professionals, counterterrorism experts, and policy makers. The monograph can also serve as a reference material or textbook in graduate level courses related to information security, information policy, information assurance, information systems, terrorism, and public policy.