In this paper we present a generalized approach to the decoupling problems of linear systems, such that both time-varying and time-invariant systems, scalar and block decoupling problems, may be studied in the same framework. We also derive the necessary and sufficient conditions for a linear system to be decoupled by output feedback only. Use of a state estimator, when some of the plant states are inaccessible, and the possibility of the reduction of its order are next studied. The results derived are illustrated by several examples.