Keywords: Explanation, Operationality, Learning Systems: An example uses LEX and there is some discussion of Winston's ANALOGY and Lebowitz's UNIMEM. Summary: Contrasts relatively weak "similarity-based generalization" (standard supervised learning) with "explanation-based" methods that rely on a powerful domain theory to produce deductively justifiable concept definitions. Argues that a single compact, well-defined algorithm encompasses all of the relevant features of all past work in explanation based methods. Presents this algorithm in two steps, explanation by application of deductive rules and generalization by variablizing features. Illustrates the algorithm on the safe-to-stack and cup problems. Compares EBG to Winston's ANALOGY program which also constructs generalizations but goes so using concrete examples with causal relationships encoded. Describes an example of learning search heuristics in LEX (which solves integral calculus problems). Contrasts this with a variety of single purpose heuristic learning systems. Presents different views of EBG (learning, generalization, operationalized reformulation, etc.). Discusses open research problems such as imperfect theories, combining EBG with similarity-based methods (e.g. UNIMEM which verifies empirical generalizations by attempting to construct explanations), integrating EBG into larger problems (discussing LEX2 and METALEX). In an appendix, describes DeJong's work on explanation-based generalization for story understanding.