The network representation learning algorithm represents the information network as a low-dimensional dense real vector carrying the characteristic information of network nodes, and is applied to the input of downstream machine learning tasks. With the development of machine learning and deep learning, network representation learning has been widely used due to its powerful modeling capabilities and extensive applications. The network representation learning methods and their application were summarized. Firstly, the current network representation learning methods at home and abroad were categorized into different groups, including traditional methods, network structure-based embedding, embedding with attribute information, and spectral-based Graph Convolutional Networks, spatial-based Graph Convolutional Networks and Graph Attention Networks. Then various models were expounded, and the applicability and characteristics of the models were compared. Secondly, the related applications of network representation learning, including recommender system and biomedical field, were introduced. Commonly used data sets are also given, and open source implementations of representation learning models and powerful graph deep learning libraries for reference were organized. Finally, the developing trend of network representation learning was summarized and forecasted. Deep graph neural network, dynamic and heterogeneous network representation, and generalization ability of network model will need to be further studied.