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Entity-relationship extraction has gained more and more attention from researchers as a basis for knowledge graph construction. Entity-relationship extraction can automatically and accurately obtain knowledge from a large amount of data, and represent and store it in a structured form. Therefore, the correctness of entity-relationship extraction directly affects the accuracy of knowledge graph construction and the effect of subsequent knowledge graph application. However, for different research hotspots such as complex structure, open domain, multi-language, multi-modal, small sample data, and joint extraction of entity-relationships, the existing entity-relationship extraction methods still have some limitations. Based on the current research hotspots of entity-relationship extraction, this paper tries to categorize entity-relationship extraction into six aspects: complex structure, open domain, multilingual, multimodal, small-sample data, and joint entity-relationship extraction, and categorizes each aspect according to the specific problems and lists out some solutions. Not only the current problems and solutions of each category are systematically sorted out, but the research results of each category are summarized, and the advantages and disadvantages of each method are analyzed in detail from the dimensions of quantitative analysis and qualitative analysis. Finally, the problems to be solved in the current hot areas are summarized, and the future development trend of entity-relationship extraction methods in the knowledge graph is also prospected.