Knowledge Graph (KG) strongly support the research of knowledge-driven artificial intelligence. Aiming at this fact, the existing technologies of knowledge graph and knowledge hypergraph were analyzed and summarized. At first, from the definition and development history of knowledge graph, the classification and architecture of knowledge graph were introduced. Second, the existing knowledge representation and storage methods were explained. Then, based on the construction process of knowledge graph, several knowledge graph construction techniques were analyzed. Specifically, aiming at the knowledge reasoning, an important part of knowledge graph, three typical knowledge reasoning approaches were analyzed, which are logic rule-based, embedding representation-based, and neural network-based. Furthermore, the research progress of knowledge hypergraph was introduced along with heterogeneous hypergraph. To effectively present and extract hyper-relational characteristics and realize the modeling of hyper-relation data as well as the fast knowledge reasoning, a three-layer architecture of knowledge hypergraph was proposed. Finally, the typical application scenarios of knowledge graph and knowledge hypergraph were summed up, and the future researches were prospected.