Abstract A conceptual graph (CG) is a graph representation for logic based on the semantic networks of artificial intelligence and the existential graphs of Charles Sanders Peirce. CG design principles emphasize the requirements for a cognitive representation: a smooth mapping to and from natural languages; an “iconic” structure for representing patterns of percepts in visual and tactile imagery; and cognitively realistic operations for perception, reasoning, and language understanding. The regularity and simplicity of the graph structures also support efficient algorithms for searching, pattern matching, and reasoning. Different subsets of conceptual graphs have different levels of expressive power: the ISO standard conceptual graphs express the full semantics of Common Logic (CL), which includes the subset used for the Semantic Web languages; a larger CG subset adds a context notation to support metalanguage and modality; and the research CGs are exploring an open-ended variety of extensions for aspects of natural language semantics. Unlike most notations for logic, CGs can be used with a continuous range of precision: at the formal end, they are equivalent to classical logic; but CGs can also be used in looser, less disciplined ways that can accommodate the vagueness and ambiguity of natural languages. This chapter surveys the history of conceptual graphs, their relationship to other knowledge representation languages, and their use in the design and implementation of intelligent systems.