System self-explanation is critical for the construction, utility, acceptance, and maintenance of complex, knowledge-based software. This paper presents a new methodology and implementation techniques that enable software systems to explain their knowledge and reasoning, i.e., to become "self-revealing." The theory addresses the spectrum of explanation goals and is applicable to complex and unstructured domains and to general control structures. The method, called REVEAL, represents the culmination of research and experimentation with new explanation techniques conducted as part of the development of a legal expert system, SAL (System for Asbestos Litigation). SAL adheres to the design philosophy of REVEAL and utilizes many of the associated techniques. Throughout the dissertation, the theoretical concepts are demonstrated by examples of their implementation in SAL.