Abstract: In the context of carbon neutrality and emission peak, the power system with high penetration of renewable energy will become one important development trend of future power system. In addition, extreme weather events occur with high variability and frequency. Power systems, in consequence, have more and more uncertainties, that have great impacts on economical, safe and stable system operation. It is necessary to analyze these impacts and the corresponding measures based on the stochastic characteristics. From the perspectives of stochastic variables and system equations, the power system stochastic problems are divided into three categories of stochastic steady state problem, stochastic dynamic problem and stochastic event problem. The description and analysis methods are presented for these three types of problems, respectively. For the power system stochastic steady state problem, the system stochastic steady state analysis method is presented from the perspective of stochastic feature analysis and stochastic decision problem. For the power system stochastic dynamic problem, the impacts of stochastics on dynamics from oscillation, security, and stability are reviewed and discussed. For the power system stochastic event problem, a survey on probabilistic analysis and Markov analysis is performed. Finally, the future trend of probabilistic forecasting for renewables, system stochastic planning and operation, anti-disturbance capability with low inertia, stochastic dynamics, and impacts of extreme weather on renewables are discussed.