With the rise of deep neural network， Deep Metric Learning （DML） has attracted widespread attention. To gain a deeper understanding of deep metric learning， firstly， the limitations of traditional metric learning methods were organized and analyzed. Secondly， DML was discussed from three types， including types based on sample pairs， proxies， and classification. Divergence methods， ranking methods and methods based on Generative Adversarial Network （GAN） were introduced in detail of the type based on sample pairs. Proxy-based types was mainly discussed in terms of proxy samples and categories. Cross-modal metric learning， intra-class and inter-class margin problems， hypergraph classification， and combinations with other methods （such as reinforcement learning-based and adversarial learning-based methods） were discussed in the classification-based type. Thirdly， various metrics for evaluating the performance of DML were introduced， and the applications of DML in different tasks， including face recognition， image retrieval， and person re-identification， were summarized and compared. Finally， the challenges faced by DML were discussed and some possible solution strategies were proposed.