Electrified aircraft propulsion (EAP) systems hold potential for the reduction of aircraft fuel burn, emissions, and noise. Currently, NASA and other organizations are actively working to identify and mature technologies necessary to bring EAP designs to reality. This paper specifically focuses on the envisioned control technology challenges associated with EAP designs that include gas turbine technology. Topics discussed include analytical tools for the dynamic modeling and analysis of EAP systems, and control design strategies at the propulsion and component levels. This includes integrated supervisory control facilitating the coordinated operation of turbine and electrical components, control strategies that seek to minimize fuel consumption and lessen the challenges associated with thermal management, and dynamic control to ensure engine operability during system transients. These dynamic control strategies include innovative control approaches that either extract or supply power to engine shafts dependent upon operating phase, which may improve performance and reduced gas turbine engine weight. Finally, a discussion of control architecture design considerations to help alleviate the propulsion/aircraft integration and certification challenges associated with EAP systems is provided.