For a pair of continuous linear operatorsTandSon complex Banach spacesXandY, respectively, this paper studies the local spectral properties of the commutatorC(S, T) given byC(S, T)(A): =SA−ATfor allA∈L(X, Y). Under suitable conditions onTandS, the main results provide the single valued extension property, a description of the local spectrum, and a characterization of the spectral subspaces ofC(S, T), which encompasses the closedness of these subspaces. The strongest results are obtained for quotients and restrictions of decomposable operators. The theory is based on the recent characterization of such operators by Albrecht and Eschmeier and extends the classical results for decomposable operators due to Colojoară, Foiaş, and Vasilescu to considerably larger classes of operators. Counterexamples from the theory of semishifts are included to illustrate that the assumptions are appropriate. Finally, it is shown that the commutator of two super-decomposable operators is decomposable.