Magnetotelluric (MT) inversion is a key technology for exploration underground electrical structures. However, conventional methods such as the Gauss-Newton method and Occam method are limited by high computational complexity, sensitivity to initial models, and strong non-uniqueness. In recent years, deep learning has significantly improved the efficiency and accuracy of inversion through end-to-end nonlinear mapping, multimodal data fusion, and noise enhancement strategies. This paper systematically reviews the core progress of deep learning in MT inversion: Firstly, it reviews five traditional MT inversion methods, including the Gauss-Newton method, quasi-Newton method, Occam method, conjugate gradient method, and nonlinear conjugate gradient method. These conventional MT inversion methods face problems such as high computational resource requirements, significant sensitivity to initial models, and strong non-uniqueness. Then, in response to these difficulties, this paper mainly reviews the application of deep learning methods such as MT2DInv-Unet and MT-MitNet in MT inversion. MT2DInv-Unet avoids the dependence on initial models through end-to-end nonlinear mapping, reduces the risk of falling into local optimal solutions, and thus alleviates the problems of initial model sensitivity and strong non-uniqueness; MT-MitNet accelerates forward modeling, significantly shortening the forward calculation time and effectively reducing computational complexity. The application of deep learning methods effectively improves the predicament of traditional inversion methods. Finally, in the face of challenges such as scarce measured data, non-Gaussian noise interference, and three-dimensional anisotropic modeling in complex geological scenarios, this paper combines the advantages of deep learning methods and proposes targeted suggestions for optimizing MT inversion.