The development of the Internet of Things, cloud computing, and artificial intelligence has given birth to industrial artificial intelligence (IAI) technology, which enables us to obtain fine perception and in-depth understanding capabilities for the operating conditions of industrial processes, and promotes the intelligent transformation of modern industrial production processes. At the same time, modern industry is facing diversified market demand instead of ultra-large-scale demand, resulting in typical variable conditions, which enhances the nonstationary characteristics of modern industry, and brings great challenges to the monitoring of industrial processes. In this regard, this paper analyzes the complex characteristics of nonstationary industrial operation, reveals the effects on operating condition monitoring, and summarizes the difficulties faced by varying condition monitoring. Furthermore, by reviewing the recent 30 years of development of data-driven methods for industrial process monitoring, we sorted out the evolution of nonstationary monitoring methods, and analyzed the features, advantages and disadvantages of the methods at different stages. In addition, by summarizing the existing related research methods by category, we hope to provide reference for monitoring methods of nonstationary process. Finally, combined with the development trend of industrial artificial intelligence technologies, some promising research directions are given in the field of nonstationary process monitoring.