Abstract: The scientific evolution of weather forecasts is briefly reviewed from a historical perspective in this paper. During the last 100 years, applications of weather maps (surface and upper air) and numerical weather prediction (NWP) to daily weather forecasts marked two major achievements: weather maps expanded our view from two dimensions to three dimensions in space and NWP brought us ahead of real weather in time. Through these advancements, weather forecasting has gradually evolved from an empirical to a qualitatively-reasoning and further to an exact physical science based on mathematical equations. With the discovery of chaos by Prof. Edward Lorenz, weather forecasting is now undergoing its third philosophical revolution from a deterministic to probabilistic world to facing the reality of its limited predictability. Two different approaches are presented, as the main focus of this paper, to deal with the limitation of predictability and forecast uncertainty: one is using ensemble forecasting technique to directly quantify and include forecast uncertainty information in a forecast which can be utilized by endusers to make better decisions; the other is an attempt to have a workaround of nonlinearity mathematically by decomposing a meteorological fi eld into climatic and anomalous two components. Therefore, weather forecasting could be possibly simplified in dealing with the anomalous components only.