The potato is a key crop in addressing global hunger, and deep learning is at the core of smart agriculture. Applying deep learning (e.g., YOLO series, ResNet, CNN, LSTM, etc.) in potato production can enhance both yield and economic efficiency. Therefore, researching efficient deep learning models for potato production is of great importance. Common application areas for deep learning in the potato production chain, aimed at improving yield, include pest and disease detection and diagnosis, plant health status monitoring, yield prediction and product quality detection, irrigation strategies, fertilization management, and price forecasting. The main objective of this review is to compile the research progress of deep learning in various processes of potato production and to provide direction for future research. Specifically, this paper categorizes the applications of deep learning in potato production into four types, thereby discussing and introducing the advantages and disadvantages of deep learning in the aforementioned fields, and it discusses future research directions. This paper provides an overview of deep learning and describes its current applications in various stages of the potato production chain.