Alzheimer's disease (AD) affects millions of individuals worldwide and is considered a serious global health issue due to its gradual neuro-degenerative effects on cognitive abilities such as memory, thinking, and behavior. There is no cure for this disease but early detection along with a supportive care plan may aid in improving the quality of life for patients. Automated detection of AD is challenging because its symptoms vary in patients due to genetic, environmental, or other co-existing health conditions. In recent years, multiple researchers have proposed automated detection methods for AD using MRI and fMRI. These approaches are expensive, have poor temporal resolution, do not offer real-time insights, and have not proven to be very accurate. In contrast, only a limited number of studies have explored the potential of Electroencephalogram (EEG) signals for AD detection. In contrast, Electroencephalogram (EEG) signals present a cost-effective, non-invasive, and high-temporal-resolution alternative for AD detection. Despite their potential, the application of EEG signals in AD research remains under-explored. This study reviews publicly available EEG datasets, the variety of machine learning models developed for automated AD detection, and the performance metrics achieved by these methods. It provides a critical analysis of existing approaches, highlights challenges, and identifies key areas requiring further investigation. Key findings include a detailed evaluation of current methodologies, prevailing trends, and potential gaps in the field. What sets this work apart is its in-depth analysis of EEG signals for Alzheimer's Disease detection, providing a stronger and more reliable foundation for understanding the potential role of EEG in this area.