Drug discovery is the process of new drug identification. This process is driven by the increasing data from existing chemical libraries and data banks. The knowledge graph is introduced to the domain of drug discovery for imposing an explicit structure to integrate heterogeneous biomedical data . The graph can provide structured relations among multiple entities and unstructured semantic relations associated with entities. In this review, we summarize knowledge graph-based works that implement drug repurposing and adverse drug reaction prediction for drug discovery. As knowledge representation learning is a common way to explore knowledge graphs for prediction problems, we introduce several representative embedding models to provide a comprehensive understanding of knowledge representation learning.