Drowsiness is a state of fatigue or sleepiness characterized by a strong urge to sleep. It is correlated with a progressive decline in response time, compromised processing of available information, more errors in short-term memory, and reduced vigilance behaviors. The electroencephalogram (EEG), a recording of the brain’s electrical activities, has demonstrated the most robust association with drowsiness. As a result, EEG is widely recognized as a dependable indicator for evaluating drowsiness, fatigue, and performance levels. In this survey paper, we thoroughly investigate the application of shallow and deep neural network approaches utilizing EEG signals for the detection of fatigue and drowsiness. As far as our knowledge extends, this is the pioneering survey paper dedicated to exploring this specific research domain. The paper presents a comprehensive overview of the diverse EEG features utilized in the detection of fatigue and drowsiness, the different types of neural networks, and the reported performance of these methods in the literature. Additionally, the paper thoroughly examines the challenges and limitations associated with EEG-based fatigue and drowsiness detection and highlights directions for future research. The survey aims to offer a comprehensive overview of the existing methods in EEG-based fatigue and drowsiness detection, serving as a valuable resource for researchers and practitioners working in the respective field.