The objective of this paper is to review supervisory Discrete Event Systems (DES) control framework in a hybrid perspective for integrated control of aircraft propulsion, thermal, and power systems. Supervisory control of DES research area for aircraft propulsion and power systems is motivated by the need to solve the problem of modeling and control of large-scale complex systems in discrete-event setting. Theories of DES control in a hierarchical and hybrid framework can be implemented to incorporate continuously-varying and discrete-event dynamics. Implementation of hybrid supervisory control to integrated flight and propulsion system is reviewed. Continuous and discrete event controllers can be implemented in a hybrid setting to regulate both integrated system dynamics and operational behaviors. Supervisory DES control architecture can be designed for a multiple-engine propulsion system integrated with aircraft power, thermal management, and weapon subsystems. This control architecture is capable of assessing conditions of turbine engines/subsystems and also capable of tracking their operational performance for onboard diagnostics and prognostics.