Alzheimer’s Disease (AD) and Mild Cognitive Impairment (MCI) are neurodegenerative conditions that severely affect cognition and quality of life. With the increasing prevalence of dementia worldwide, there is an urgent need for accessible, accurate, and non-invasive diagnostic methods. Electroencephalography (EEG) has emerged as a promising tool for early detection due to its cost-effectiveness and ability to capture brain activity in real time. This systematic review examines the application of deep learning techniques—specifically Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and transformers—on EEG data for the early detection of AD and MCI. A total of 116 studies were initially identified from PubMed, IEEE Xplore, and ScienceDirect, and after filtering for relevance, 29 papers were selected for this review. These studies explored various deep learning architectures and preprocessing techniques, highlighting the effectiveness of CNNs in capturing spatial patterns, RNNs in modeling temporal dynamics, and transformers in managing long-range dependencies in EEG data. This review provides a comprehensive overview of the current landscape, identifies key challenges such as generalizability and interpretability, and discusses future directions in EEG-based AD/MCI detection. Readers will gain insights into which methods are best suited for specific applications.