Alzheimer’s disease (AD) is a prominent neurocognitive disorder, affecting over 55 million people globally, with an annual rise of 10 million new cases according to the WHO’s March 2023 report. It is the seventh leading cause of death worldwide and significantly contributes to disability and dependency in older adults. Classified into seven stages, the disease is often diagnosed at stage 4, where moderate cognitive impairment limits patients’ ability to perform daily tasks independently. As the disease progresses, individuals experience severe memory loss, impaired recognition, and the need for continuous caregiver support. This review examines the latest deep learning methodologies employed to detect and classify Alzheimer’s disease based on severity, focusing on hippocampal atrophy, a key biomarker for AD. The study explores three critical steps in AD detection using MRI and CT scan images: acquiring and preprocessing data, segmenting relevant brain regions (such as the hippocampus and amygdala), and applying deep learning techniques for the classification of subjects to inform the existence and stage of the disease in patients. Traditional deep learning approaches such as CNNs, U-Net, and ResNet are observed to most effectively capture local features and dependencies within images, with transfer learning methods being used for pre-training models to improve accuracy and robustness. In contrast, emerging transformer-based models, including SWIN Transformers and Vision Transformers, are more effective in capturing global features using multi-scale attention mechanisms, scoring equally on common performance parameters such as sensitivity, accuracy, Jaccard, and dice coefficients. Efforts to combine Transformers with CNN-based backbones are shown to give promising results over multiple datasets and aim toward addressing the most significant challenge of generalizability of models over multiple test datasets and clinical adaptability.