Airborne wind energy systems convert wind energy into electricity using tethered flying devices, typically flexible kites or aircraft. Replacing the tower and foundation of conventional wind turbines can substantially reduce the material use and, consequently, the cost of energy, while providing access to wind at higher altitudes. Because the flight operation of tethered devices can be adjusted to a varying wind resource, the energy availability increases in comparison to conventional wind turbines. Ultimately, this represents a rich topic for the study of real-time optimal control strategies that must function robustly in a spatiotemporally varying environment. With all of the opportunities that airborne wind energy systems bring, however, there are also a host of challenges, particularly those relating to robustness in extreme operating conditions and launching/landing the system (especially in the absence of wind). Thus, airborne wind energy systems can be viewed as a control system designer’s paradise or nightmare, depending on one’s perspective. This survey article explores insights from the development and experimental deployment of control systems for airborne wind energy platforms over approximately the past two decades, highlighting both the optimal control approaches that have been used to extract the maximal amount of power from tethered systems and the robust modal control approaches that have been used to achieve reliable launch, landing, and extreme wind operation. This survey will detail several of the many prototypes that have been deployed over the last decade and will discuss future directions of airborne wind energy technology as well as its nascent adoption in other domains, such as ocean energy.