Amputation of the upper limb brings heavy burden to amputees, reduces their quality of life, and limits their performance in activities of daily life. The realization of natural control for prosthetic hands is crucial to improving the quality of life of amputees. Surface electromyography (sEMG) signal is one of the most widely used biological signals for the prediction of upper limb motor intention, which is an essential element of the control systems of prosthetic hands. The conversion of sEMG signals into effective control signals often requires a lot of computational power and complex process. Existing commercial prosthetic hands can only provide natural control for very few active degrees of freedom. Deep learning (DL) has performed surprisingly well in the development of intelligent systems in recent years. The significant improvement of hardware equipment and the continuous emergence of large data sets of sEMG have also boosted the DL research in sEMG signal processing. DL can effectively improve the accuracy of sEMG pattern recognition and reduce the influence of interference factors. This paper analyzes the applicability and efficiency of DL in sEMG-based gesture recognition and reviews the key techniques of DL-based sEMG pattern recognition for the prosthetic hand, including signal acquisition, signal preprocessing, feature extraction, classification of patterns, post-processing, and performance evaluation. Finally, the current challenges and future prospects in clinical application of these techniques are outlined and discussed.