The procedure to combine mathematical models with inaccurate and noisy data, improving weather forecasting by statistical methods, is an important and challenging line of research in meteorology, known as data assimilation. Current techniques of data assimilation are based on Gaussian Least Squares Method. This paper presents the main advances in data assimilation, since the empirical methods, created in the 1950s, to the current methods, as well as their derivatives and hybrid versions. It is note that the emergence of hybrid methods ensemble/variational and improved in the satellite and radar data assimilation techniques are major advances in the field in recent years. It is concluded that the variational methods and the Kalman filtering are the state of the art of data assimilation techniques.
