The set-membership approach to the state estimation of dynamical systems subjected to uncertain disturbances is developed. Optimal outer ellipsoidal estimates on reachable sets are considered, and various optimality criteria are discussed. Nonlinear differential equations describing the evolution of optimal estimating ellipsoids are analyzed. The asymptotic behavior of the ellipsoids is investigated in the vicinity of the initial time instant and at infinity. Control problem for the systems subjected to uncertain perturbations is analyzed in the framework of the optimal ellipsoidal estimation.