Data assimilation attempts to optimally determine the state of a physical system from a limited number of observations. The extended Kalman filter (EKF) is characterized by solving the full nonlinear state evolution, and by using successive linearizations about the currently estimated state to advance the error-covariance matrix in time. It thus provides a consistent first-order approximation to the optimal estimate of the nonlinear state at the observation time. The EKF method combines the observations and modeled state variables to obtain the "assimilated" field variables with an optimal gain matrix coefficient, which is a function of the forecast error-covariance and the observational errors. The assimilated fields can be used as initial conditions for further model prediction. They can also be used inside of a model as a forcing function through a form of Newtonian nudging. In this talk, examples of applying EKF to atmospheric and oceanic systems will be given. An ongoing experiment of using EKF in shock related physical systems will be introduced.