This paper endeavors to deliver a detailed probabilistic uncertainty modeling approaches for power system planning and operation. The conventional uncertainty modeling approaches are reviewed, and the modeling challenges under large-scale integration of renewable generations are described. The modeling steps in various timescales (of the time horizons) for different applications are clarified inclusively. It is believed that the paper will help the novice readers in the probabilistic uncertainty modeling area. © 2019, Springer Nature Singapore Pte Ltd.