The application of synaptic device-based neuromorphic computing in artificial intelligence is an emerging research field aimed at simulating the structure and function of the human brain and realizing high-efficiency, low-power, and adaptive intelligent computing. This paper reviews the principles, growth and challenges of neuromorphic devices based on synapses computing and its applications and perspectives in artificial intelligence fields like an image processing as well as natural language processing. The paper first introduces the basic concepts, properties and classification of synaptic devices, as well as the basic framework and algorithms of neuromorphic computing. Then, the paper analyzes the advantages and difficulties of neuromorphic computing based on synaptic devices, including the preparation, testing, modelling and integration of the devices, as well as the systems architecture, programming and optimization. Then, this paper gives examples of the applications and effects of synaptic device-based neuromorphic computing in artificial intelligence fields such as image processing and natural language processing, including image denoising, image segmentation, image recognition, text classification, text summarization, and text generation. Finally, this paper summarizes the current research status and future synaptic device-based neuromorphic computing trends. It puts forward some research directions and suggestions to promote the development and innovation in this field.