Electro-encephalography (EEG) and electro-oculography (EOG) are methods of electrophysiological monitoring that have potentially fruitful applications in neuroscience, clinical exploration, the aeronautical industry, and other sectors. These methods are often the most straightforward way of evaluating brain oscillations and eye movements, as they use standard laboratory or mobile techniques. This review describes the potential of EEG and EOG systems and the application of these methods in aeronautics. For example, EEG and EOG signals can be used to design brain-computer interfaces (BCI) and to interpret brain activity, such as monitoring the mental state of a pilot in determining their workload. The main objectives of this review are to, (i) offer an in-depth review of literature on the basics of EEG and EOG and their application in aeronautics; (ii) to explore the methodology and trends of research in combined EEG-EOG studies over the last decade; and (iii) to provide methodological guidelines for beginners and experts when applying these methods in environments outside the laboratory, with a particular focus on human factors and aeronautics. The study used databases from scientific, clinical, and neural engineering fields. The review first introduces the characteristics and the application of both EEG and EOG in aeronautics, undertaking a large review of relevant literature, from early to more recent studies. We then built a novel taxonomy model that includes 150 combined EEG-EOG papers published in peer-reviewed scientific journals and conferences from January 2010 to March 2020. Several data elements were reviewed for each study (e.g., pre-processing, extracted features and performance metrics), which were then examined to uncover trends in aeronautics and summarize interesting methods from this important body of literature. Finally, the review considers the advantages and limitations of these methods as well as future challenges.