In this paper two topics are explored. First, a new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed, The moving horizon observer produces an estimate of the state of the nonlinear system at time t either by minimizing, or approximately minimizing, a cost function over the preceding interval (horizon) [t - T,t]; as t advances, so does the horizon, Convergence of the estimator is established under the assumption that the corresponding global optimization problem can be (approximately) solved and a uniform reconstructability condition is satisfied; the latter condition is automatically satisfied for linear observable systems, Second, the utility of the estimator for receding horizon control is explored, In particular, stability of a composite moving horizon system, comprising a moving horizon regulator and a moving horizon observer, is established.