This paper reviews the historic understanding of the predictability of atmospheric and oceanic motions, and interprets it in a general framework. On this basis, the existing challenges and unsolved problems in the study of the intrinsic predictability limit(IPL) of weather and climate events of different spatio-temporal scales are summarized. Emphasis is also placed on the structure of the initial error and model parameter errors as well as the associated targeting observation issue. Finally, the predictability of atmospheric and oceanic motion in the ensemble-probabilistic methods widely used in current operational forecasts are discussed.The necessity of considering IPLs in the framework of stochastic dynamic systems is also addressed. This paper reviews the historic understanding of the predictability of atmospheric and oceanic motions, and interprets it in a general framework. On this basis, the existing challenges and unsolved problems in the study of the intrinsic predictability limit (IPL) of weather and climate events of Different spatio-temporal scales are summarized. Emphasis is also placed on the structure of the initial error and model parameter errors as well as the associated targeting observation issue. Finally, the predictability of atmospheric and oceanic motion in the ensemble-probabilistic methods widely used in current operational forecasts are discussed.The necessity of considering IPLs in the framework of stochastic dynamic systems is also addressed.