DL has achieved great success in signal processing and communications and has become a promising technology for future wireless communications. Existing works mainly focus on exploiting DL to improve the performance of communication systems. However, the high memory requirement and computational complexity constitute a major hurdle for the practical deployment of DL-based communications. In this article, we investigate how to compress and accelerate the neural networks (NNs) in communication systems. After introducing the deployment challenges for DL-based communication algorithms, we discuss some representative NN compression and acceleration techniques. Afterwards, two case studies for multiple-input-multiple- output (MIMO) communications, including DL-based channel state information feedback and signal detection, are presented to show the feasibility and potential of these techniques. We finally identify some challenges on NN compression and acceleration in DL-based communications and provide a guideline for subsequent research.