With the development of industrial Internet technology, the data volume of industrial equipment has increased exponentially, which has brought a huge data pressure to cloud computing. There is more and more applications and researches of edge computing in the industrial field due to the characteristics of low latency, low traffic, and good privacy. We review the research on cloud computing and edge computing in industrial applications in recent years. We firstly introduce the development history of cloud computing and edge computing in the context of the industrial Internet, and analyze the definition of edge computing and the relationships between several typical forms of edge computing and industrial edge computing system. Secondly, several typical applications of industrial edge computing are analyzed. In view of the current research status, several key technologies affecting edge computing applications in industrial scenarios are discussed. Finally, the research challenges in the industrial scene are summarized and prospected.