Knowledge graph (KG), with their unique approach to knowledge management and representation capabilities, have been widely applied in various knowledge computing fields, including question answering. However, incomplete information is often present in KG, which undermines their quality and limits the performance of downstream tasks. As a result, knowledge graph completion (KGC) has emerged, aiming to enhance the quality of KG by predicting the missing information in triples using different methods. In recent years, extensive research has been conducted in the field of KGC. This study classifies KGC techniques into three categories based on the number of samples used: zero-shot KGC, few-shot KGC, and multi-shot KGC. To investigate and provide a first-hand reference for the core concepts and current status of KGC research, this study offers a comprehensive review of the latest research advancements in KGC from theoretical research, experimental analysis, and practical applications, such as the Huapu system. The problems and challenges faced by the current KGC technologies are summarized, and potential research directions for the future are discussed.