A graph structure is a powerful mathematical abstraction, which can not only represent information about individuals but also capture the interactions between individuals for reasoning. Geometric modeling and relational inference based on graph data is a long-standing topic of interest in the computer vision community. In this article, we provide a systematic review of graph representation learning and its applications in computer vision. First, we sort out the evolution of representation learning on graphs, categorizing them into the nonneural network and neural network methods based on the way the nodes are encoded. Specifically, nonneural network methods, such as graph embedding and probabilistic graphical models, are introduced, and neural network methods, such as graph recurrent neural networks, graph convolutional networks, and variants of graph neural networks, are also presented. Then, we organize the applications of graph representation algorithms in various vision tasks (such as image classification, semantic segmentation, object detection, and tracking) for review and reference, and the typical graph construction approaches in computer vision are also summarized. Finally, on the background of biology and brain inspiration, we discuss the existing challenges and future directions of graph representation learning and computer vision.