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The knowledge graph (KG) that represents structural relations among entities has become an increasingly important research field for knowledge-driven artificial intelligence. In this survey, a comprehensive review of KG and KG reasoning is provided. It introduces an overview of KGs, including representation, storage, and essential technologies. Specifically, it summarizes several types of knowledge reasoning approaches, including logic rules-based, representation-based, and neural network-based methods. Moreover, this paper analyzes the representation methods of knowledge hypergraphs. To effectively model hyper-relational data and improve the performance of knowledge reasoning, a three-layer knowledge hypergraph model is proposed. Finally, it analyzes the advantages of three-layer knowledge hypergraphs through reasoning and update algorithms which could facilitate future research.