This article discusses the transition from traditional methods to a new deep learning architecture for speaker recognition. It is aimed at comparing traditional statistical methods and new approaches using deep learning models. In addition, the latest optimization methods are described. There are also several assessment methodologies based on different approaches. The article provides an overview of deep learning methods and discusses recent literature using these approaches for speaker recognition. Speaker verification involves checking the speech signal to confirm whether the speaker's statement is true or false. Deep neural networks are one of the most successful implementations of complex nonlinear models for studying special properties of data. They demonstrated their abilities in speaker recognition and speaker recognition tasks. In this article, we will look at deep neural network (DNN) methods used in speaker verification systems. It will include the database used, the results, the contribution to speaker recognition and related limitations.