Safe, efficient, and sustainable operations and control are primary objectives in industrial manufacturing processes. State-of-the-art technologies heavily rely on human intervention, thereby showing apparent limitations in practice. The burgeoning era of big data is influencing the process industries tremendously, providing unprecedented opportunities to achieve smart manufacturing. This kind of manufacturing requires machines to not only be capable of relieving humans from intensive physical work, but also be effective in taking on intellectual labor and even producing innovations on their own. To attain this goal, data analytics and machine learning are indispensable. In this paper, we review recent advances in data analytics and machine learning applied to the monitoring, control, and optimization of industrial processes, paying particular attention to the interpretability and functionality of machine learning models. By analyzing the gap between practical requirements and the current research status, promising future research directions are identified.