In this Chapter, the general discrete-continuous observation control problem is formulated. In this class of problems, a single discrete observation plays the role of an impulse control and induces a discontinuity of the estimate and its covariance. We prove existence theorems of the optimal control and give a representation of the solution in the form of a nonlinear differential equation with a measure. We establish convexity properties of this problem with constraints and then derive necessary and sufficient optimality conditions. We give examples of various observation control problems and show how the methods of impulse control help to solve various problems, for example, determining of power and composition of the sounding impulse in radar systems.