Publisher Summary The development of the concept of model-based systems was an answer to the limitations of rule-based expert systems, which base problem solving (e.g., diagnosis) on a representation of experiential knowledge in a domain. These limitations are not due to the syntactic form of representing knowledge (rules), but they result from the nature of the represented knowledge termed “empirical associations” in the pioneering paper or “shallow knowledge” in others. This chapter discusses the key ideas of selected solutions with some formalization and, perhaps, some hints on a possible implementation. In discusses solutions that address the important requirements of the application context in a principled and general way over approaches that are heavily influenced by specific features of a particular application domain or that fail to reflect essential conditions of a real-world task. Diagnosis is only a step toward the real goal, which is restoring the functionality of a disturbed system. To be effective in the framework of consistency-based problem solving, completeness matters—that is, its ability to detect all existing (or relevant) inconsistencies.