Abstract: Model predictive control (MPC) is an optimal control algorithm with stability guarantees, but it requires solving optimization problems online, which greatly limits its deployment in embedded systems. Thanks to the development of deep learning and computational hardware, neural network approximation MPC method with offline training and online inference has received widespread attention and has shown excellent performance in actual control systems. This paper discusses the latest progress on two key issues: 1) the design of neural network structures, dataset generation, and training methods; 2) methods for dealing with neural network approximation errors to ensure closed-loop system stability and constraint satisfaction. Finally, we present case studies of fast deployment of neural networks on GPU and FPGA, demonstrating the practical performance advantages of using neural networks to approximate MPC.