In this paper, the problem of supervisory control of discrete-event systems (DES) with output is presented and discussed at length. In such systems, causal output maps are employed to assign to each sequence of input events a corresponding sequence of output events. When the specification of desired behaviour is given by a formal language over the output alphabet, necessary and sufficient conditions are derived for the existence of non-blocking input as well as non-blocking output supervisory control. After making minor adjustments the theory is applied to non-deterministic discrete-event abstractions of hybrid systems, giving rise to the development of a theory for non-blocking supervisory control of hybrid systems. Our results enable one to apply classical supervisory control theory to design supervisors for DES approximations of hybrid systems, and to import many interesting concepts from classical theory such as modular and hierarchical control.