Currently, with the in-depth integration of new-generation artificial intelligence technologies and advanced control theories, the control paradigm for complex industrial processes is undergoing rapid iteration, which has not only promoted the development and refinement of the theoretical system for the safe operation control of complex industrial processes, but also provided strong support for the large-scale implementation of intelligent control systems. Based on the backdrop of industrial intelligence, this paper focuses on the integrated requirements of complex industrial processes, namely holographic perception, anomaly diagnosis, autonomous decision-making, dynamic regulation, and collaborative optimization. It systematically clarifies the basic connotations, principles, key problems and research difficulties of the relevant theoretical methods for safe operation control of complex industrial processes, and summarizes the related research progress by category. On this basis, the paper explores the urgent core issues that need to be addressed in this research field, and discusses the feasible approaches to interpretable and trustworthy intelligent safe operation control driven by human-machine integration as well as the combination of knowledge and data. A preliminary verification of the relevant theoretical achievements is carried out with a typical mineral processing process as the case study. Finally, the future development trends of the safe operation control for complex industrial processes are prospected.