Atmospheric models, as well as other similar mathematical models, often have deficiencies in the form of random and/or systematic errors, as well as in the form of unknown empirical parameters. If these errors are large, they could have adverse effects on the research results, as well as on the operational forecasts performed employing such models. Advanced data assimilation methods based on Kalman filter theory and state augmentation approach can extract valuable information from the observations to successfully estimate and correct model errors. Model error estimation results employing simple one-dimensional models (KdVB, NASA's GEOS column model), as well as complex atmospheric models (such as Eta and RAMS) will be presented and discussed. We will also explain the benefits of the model error estimation process in detecting and correcting model errors when developing new atmospheric models.