With the large-scale development of clean energy, the integration of wind and solar power is increasing, and multi-energy complementary systems involving hydro, wind, and solar power are becoming more widely applied. However, accurately modeling the uncertainty in the output of these energy sources, as well as load growth, poses significant challenges for the safe and economical operation, dispatch, and planning of power grids. Characterizing this uncertainty using traditional probabilistic modeling and artificial intelligence technologies is crucial for advancing uncertainty-based optimization techniques in modern power systems. This paper presents a comprehensive review of the current research on renewable energy uncertainty characterization. First, it introduces the concept of uncertainty quantification and explores the coupling relationship between renewable energy sources and meteorological factors, along with relevant quantification methods. It then discusses the basic concepts of renewable energy uncertainty in power systems from the perspectives of research objects and mathematical problems, reviewing existing research methods, assessment indicators, and the application of typical scenarios. Finally, it summarizes the current research challenges and discusses future development trends and directions, aiming to provide references and insights for related studies.