Due to the great influence of both global climate change and human activities, climatic and hydrological processes in many basins and regions worldwide show obviously nonstationary variability, which has obvious impact on diverse practical water activities such as the hydrological simulation and forecasting, hydrological and hydraulic designs, hydrological risk evaluation and adaption, and water resources planning and management, and also affect the socioeconomic developments as well as people's lives. Over the last decade, nonstationarity in hydrological process has been becoming a hot and frontier topic in the studies of hydrology and global climate change. However, those basic and major issues on the scientific topic have not been systemically studied, and some understandings about it are limited. In this article, we mainly focused on several major issues about the studies of hydrological nonstationarity. First, we discussed and clarified the difference between the stability of hydrological system and the hydrological nonstationarity. It is pointed out that the former is mainly to study whether the physical hydrological system in a basin keeps its stability under the impacts of both climate change and human activities, which is usually quantified by the deterministic characteristics of hydrological processes, and then simulated by proper physical hydrological models. However, the hydrological nonstationarity is mainly to study whether the statistical characteristics of stochastic hydrological process is changed, including not only the nonstationarity in stochastic components, but also the nonstationarity in deterministic components of hydrological process. Then, we further discussed some key issues about the topic of hydrological nonstationarity, mainly including the research objects, expressing ways, determining criteria, and identification and description methods. We finally pointed out that the studies of hydrological nonstationarity should focus on the stochastic components of hydrological process and the hydrological extremes (droughts, rainstorms, floods, waterlogs and others), but not the deterministic characteristics of hydrological process. All the first, second and third statistical moments (i.e., the mathematical mean, variance, and coefficient of skewness) of hydrological process should at least be carefully evaluated to judge its stationary characters. In practice, both the statistical methods (unit root test, etc.) and stochastic methods can be used for the study of hydrological nonstationarity, that is, we can first identify and remove those periodic and trend components of hydrological time series using proper stochastic methods, and then judge the nonstationary characteristics of stochastic components in series using statistical test methods. Those methods used for the identification of periodicities in hydrological time series usually include the Fourier transform, variance spectral density analysis, and the maximum entropy spectral analysis. Those methods for the trend analysis of hydrological time series mainly include the Mann-Kendall test, Spearman rank correlation test, linear regress test, moving-average test, and the wavelet-based test. The results can be a basis of stochastic simulation and hydrological forecasting. However, during the analysis process the uncertainty in these results should be carefully taken into consideration. As a result, we gave several suggestions and opinions on the future researches of hydrological nonstationarity.