Abstract: The combined effects of model errors, initial condition errors and the instability of nonlinear systems lead to uncertainties in forecasting for the atmosphere, ocean and their coupled systems. In order to reduce the above negative effects on numerical weather prediction as much as possible, the methods of ensemble and assimilation have been proposed and continuously developed and applied in modern weather and climate prediction. This paper reviews the histories and applications of the main theories and methods for ensemble forecasting and data assimilation. We also introduce some progress and academic frontiers carried out by relevant institutions such as ECMWF. With the development of the theories and methods, limited space is left for traditional methods to achieve significant progress in the short term, while the fusion of emerging technologies such as artificial intelligence (AI) has attracted widespread attention and is expected to make breakthroughs.