The study on concept is now becoming a hot topic in Computational Linguistics, Natural Language Processing and Artificial Intelligence. As early as ancient Greek times, philosophers started to think about the issue of concept such as definition, features and boundary, and gradually formed Aristotle's Classical Concept View. After modern Linguistics and Language Philosophy came into being, concept is studied intensively in different fields. On the one hand, the Logical Analysis School of Language Philosophy defines and studies concept by distinguishing the object and concept in the sentences, while the Concept Analysis School focuses on the analysis of concept from the meaning of words. Both believe that concept and language are inseparable, and it is impossible to talk about concept without language, thus pushing the research of concept forward. On the other hand, researching concept from the perspective and method of linguistics has broadened the boundaries of concept research and formed new linguistic theories. Conceptual Dependency Theory believes that each unit of human language is composed of concepts, through which conceptual expressions can describe meaning and then describe human behavior. Based on Function-effect Chain, Hierarchical Network of Concepts Theory proposes a four-layer system of language concept space. It is used to express the interconnection among concepts and help computers to process natural language. Studying concept in Linguistics and Language Philosophy, demonstrating the development of research on concept, revealing the misunderstandings and errors in concept studies can provide references and guidelines for further theoretical research on Natural Language Understanding, Cognitive Intelligence and applied research on Natural Language Processing.