With the development of deep learning， speaker verification has made great progress. Compared with other biometric identification technologies， this technology has advantages of remote operation， low cost， easy human-computer interaction， etc.， thus it shows a wide range of application prospects in the fields of public security， criminal investigation， and financial services. A systematic overview of the development lineage of deep learning-based speaker verification techniques is provided. Firstly， the development history and research status of deep learning-based speaker representation model are introduced in four aspects： Model input and structure， pooling layer， supervised loss function， and self-supervised learning and pre-training model. Then， the challenges faced by speaker verification are discussed， such as cross-domain mismatch problems like noise interference， channel mismatch and far-field speech， and the corresponding domain adaptation and domain generalization methods are outlined. Finally， the further research directions are presented.