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Effective graph analysis methods can reveal the intrinsic characteristics of graph data. However, graph is non-Euclidean data, which leads to high computation and space cost while applying traditional methods. Graph embedding is an efficient method for graph analysis. It converts original graph data into a low-dimensional space and retains key information to improve the performance of downstream tasks such as node classification, link prediction, and node clustering. Different from previous studies, this paper focuses on both static and dynamic graph embedding. Firstly, this paper proposes a universal taxonomy of static and dynamic methods, including matrix factorization based methods, random walk based methods, autoencoder based methods, graph neural networks (GNN) based methods and other embedding methods. Secondly, this paper analyzes the theoretical relevance of static and dynamic methods, and comprehensively summarizes the core strategy, downstream tasks and datasets. Finally, this paper proposes four potential research directions of graph embedding.