Knowledge graphs manage and organize data and information in a structured form, which can provide effective support for various applications and services. Only reliable knowledge can provide valuable information. However, most existing knowledge graphs encounter the problem of partially unreliable knowledge. With the progress of the Internet and information technology, how to ensure the reliability of knowledge graphs has become a significant research topic. We first clarify the concept of knowledge graph reliability based on the attributes of facts in knowledge graphs. It includes two parts: the correctness and uncertainty of knowledge. We then analyze their corresponding research tasks. The research of knowledge correctness aims to handle the erroneous triples in knowledge graphs, whereas the research of knowledge uncertainty assesses the ambiguous and probabilistic triples. Knowledge representation learning, a neural technique to process symbolic knowledge, is the promising approach in the research of knowledge graph reliability. Therefore, we summarize the related studies on knowledge correctness and uncertainty based on the framework of knowledge representation learning, which includes four categories: score function modification, representation vector optimization, loss function adjustment, and textual information integration. Additionally, we present an analysis of the widely used benchmarks, and lastly conclude with a discussion on the potential trends and future research directions in the reliability of knowledge graph.