Abstract: As a method that converts graph structure into vector representations, graph representation learning has gained significant attention in recent years in various fields such as social networks, biological networks, world trade webs, and computer networks． To document the development of graph representation learning, and to provide a comprehensive overview of different methods and their related applications, the present work summarizes progress in two important categories of graph representation learning: graph embedding and graph neural networks． A detailed overview of several classical algorithms is presented． Application of graph representation learning is introduced in biology, chemistry, and medicine． Challenges and future directions that graph representation learning faces are discussed．