Electromyography (EMG) has already been broadly used in human-machine interaction (HMI) applications. Determining how to decode the information inside EMG signals robustly and accurately is a key problem for which we urgently need a solution. Recently, many EMG pattern recognition tasks have been addressed using deep learning methods. In this paper, we analyze recent papers and present a literature review describing the role that deep learning plays in EMG-based HMI. An overview of typical network structures and processing schemes will be provided. Recent progress in typical tasks such as movement classification, joint angle prediction, and force/torque estimation will be introduced. New issues, including multimodal sensing, inter-subject/inter-session, and robustness toward disturbances will be discussed. We attempt to provide a comprehensive analysis of current research by discussing the advantages, challenges, and opportunities brought by deep learning. We hope that deep learning can aid in eliminating factors that hinder the development of EMG-based HMI systems. Furthermore, possible future directions will be presented to pave the way for future research.