In aviation, any detail can have massive consequences. Among the potential sources of failure, human error is still the most troublesome to handle. Therefore, research concerning the management of mental workload, attention, and stress is of special interest in aviation. Recognizing conditions in which a pilot is over-challenged or cannot act lucidly could avoid serious outcomes. Furthermore, knowing in depth a pilot’s neurophysiological and cognitive–behavioral responses could allow for the optimization of equipment and procedures to minimize risk and increase safety. Furthermore, it could translate into a general enhancement of both the physical and mental well-being of pilots, producing a healthier and more ergonomic work environment. This review brings together literature on the study of stress and workload in the specific case of pilots of both civil and military aircraft. The most common approaches for studying these phenomena in the avionic context are explored in this review, with a focus on objective methodologies (e.g., the collection and analysis of neurophysiological signals). This review aims to identify the pros, cons, and applicability of the various approaches, to enable the design of an optimal protocol for a comprehensive study of these issues.