Deep learning based on neural networks has been widely used in image recognition, speech recognition, natural language processing, automatic driving, and other fields and has made breakthrough progress. FPGA stands out in the field of accelerated deep learning with its advantages such as flexible architecture and logic units, high energy efficiency ratio, strong compatibility, and low delay. In order to track the latest research results of neural network optimization technology based on FPGA in time and to keep abreast of current research hotspots and application fields, the related technologies and research contents are reviewed. This paper introduces the development history and application fields of some representative neural networks and points out the importance of studying deep learning technology, as well as the reasons and advantages of using FPGA to accelerate deep learning. Several common neural network models are introduced. Moreover, this paper reviews the current mainstream FPGA-based neural network acceleration technology, method, accelerator, and acceleration framework design and the latest research status, pointing out the current FPGA-based neural network application facing difficulties and the corresponding solutions, as well as prospecting the future research directions. We hope that this work can provide insightful research ideas for the researchers engaged in the field of neural network acceleration based on FPGA.