The paper proposes a perspective on knowledge compilation, focusing on two key dimensions: the succinctness of the target compilation language and the class of queries and transformations supported in polytime. It introduces a knowledge compilation map that analyzes a wide range of target compilation languages based on their succinctness and polytime transformations and queries. The authors argue that this analysis is crucial for placing new compilation approaches within the context of existing ones. They also extend the discussion beyond classical, flat target compilation languages based on CNF and DNF, considering a richer, nested class based on directed acyclic graphs (DAGs), such as OBDDs, which include a significant number of target compilation languages. The paper is structured into several sections, starting with an introduction that highlights the importance of knowledge compilation in addressing computational intractability in propositional reasoning. It defines the key aspects of knowledge compilation approaches and outlines the main contributions of the paper, which include a comprehensive analysis of various target compilation languages and a methodology for selecting the most suitable language for specific applications. The second section formally defines the NNF language, which is a complete language for representing propositional sentences using DAGs. The authors distinguish between representation languages and target compilation languages, emphasizing that the latter should be tractable enough to support polytime queries and transformations. The third section discusses the succinctness of compiled theories, providing a pre-ordering of different target compilation languages based on their succinctness. The authors show that adding properties like decomposability, determinism, and smoothness to NNF reduces its succinctness. The fourth section evaluates the suitability of target compilation languages for specific applications by considering the set of queries and transformations they support in polytime. It includes tests for consistency, validity, implicates, implicants, equivalence, sentential entailment, counting, and enumerating models. The fifth section focuses on transformations that can be applied to compiled theories, including conjunction, disjunction, negation, conditioning, and forgetting. It provides a comprehensive analysis of how these transformations are supported by different target compilation languages. The conclusion summarizes the main contributions of the paper, including a methodology for analyzing propositional compilation approaches and a comprehensive map of target compilation languages. The authors also highlight the uniform treatment of diverse target compilation languages, showing how they are subsets of the DNF language and how combinations of properties lead to different languages. The appendix contains proofs of key lemmas used in the paper.The paper proposes a perspective on knowledge compilation, focusing on two key dimensions: the succinctness of the target compilation language and the class of queries and transformations supported in polytime. It introduces a knowledge compilation map that analyzes a wide range of target compilation languages based on their succinctness and polytime transformations and queries. The authors argue that this analysis is crucial for placing new compilation approaches within the context of existing ones. They also extend the discussion beyond classical, flat target compilation languages based on CNF and DNF, considering a richer, nested class based on directed acyclic graphs (DAGs), such as OBDDs, which include a significant number of target compilation languages. The paper is structured into several sections, starting with an introduction that highlights the importance of knowledge compilation in addressing computational intractability in propositional reasoning. It defines the key aspects of knowledge compilation approaches and outlines the main contributions of the paper, which include a comprehensive analysis of various target compilation languages and a methodology for selecting the most suitable language for specific applications. The second section formally defines the NNF language, which is a complete language for representing propositional sentences using DAGs. The authors distinguish between representation languages and target compilation languages, emphasizing that the latter should be tractable enough to support polytime queries and transformations. The third section discusses the succinctness of compiled theories, providing a pre-ordering of different target compilation languages based on their succinctness. The authors show that adding properties like decomposability, determinism, and smoothness to NNF reduces its succinctness. The fourth section evaluates the suitability of target compilation languages for specific applications by considering the set of queries and transformations they support in polytime. It includes tests for consistency, validity, implicates, implicants, equivalence, sentential entailment, counting, and enumerating models. The fifth section focuses on transformations that can be applied to compiled theories, including conjunction, disjunction, negation, conditioning, and forgetting. It provides a comprehensive analysis of how these transformations are supported by different target compilation languages. The conclusion summarizes the main contributions of the paper, including a methodology for analyzing propositional compilation approaches and a comprehensive map of target compilation languages. The authors also highlight the uniform treatment of diverse target compilation languages, showing how they are subsets of the DNF language and how combinations of properties lead to different languages. The appendix contains proofs of key lemmas used in the paper.