This survey provides a comprehensive overview of deep learning methods on graphs, categorizing them into five types: graph recurrent neural networks (Graph RNNs), graph convolutional networks (GCNs), graph autoencoders (GAEs), graph reinforcement learning (Graph RL), and graph adversarial methods. The paper discusses the challenges of applying traditional deep learning to graphs, including irregular structures, heterogeneity, and scalability. It reviews the development of each method, their characteristics, and applications. The survey highlights the importance of adapting deep learning techniques to graph data, which has complex structures and relationships. It also discusses potential future research directions, emphasizing the need for systematic analysis of different methods and their integration. The paper concludes with a discussion of the key findings and the significance of graph deep learning in various domains.This survey provides a comprehensive overview of deep learning methods on graphs, categorizing them into five types: graph recurrent neural networks (Graph RNNs), graph convolutional networks (GCNs), graph autoencoders (GAEs), graph reinforcement learning (Graph RL), and graph adversarial methods. The paper discusses the challenges of applying traditional deep learning to graphs, including irregular structures, heterogeneity, and scalability. It reviews the development of each method, their characteristics, and applications. The survey highlights the importance of adapting deep learning techniques to graph data, which has complex structures and relationships. It also discusses potential future research directions, emphasizing the need for systematic analysis of different methods and their integration. The paper concludes with a discussion of the key findings and the significance of graph deep learning in various domains.