Statistical process control (SPC) charts play a central role in quality control and management. Many conventional SPC charts are designed under the assumption that the related process distribution is normal. In practice, the normality assumption is often invalid. In such cases, some articles show that certain conventional SPC charts are robust and can still be used as long as their parameters are properly chosen. Some other articles argue that results from such conventional SPC charts would not be reliable and that nonparametric SPC charts should be considered instead. In recent years, many nonparametric SPC charts have been proposed. Most of them are based on the ranking information in process observations collected at different time points. Some of them are based on data categorization and categorical data analysis. In this article, we give some perspectives on issues related to the robustness of conventional SPC charts and to the strengths and limitations of various nonparametric SPC charts.