Alzheimer’s disease (AD) is a neurological disorder that significantly impairs cognitive function, leading to memory loss and eventually death. AD progresses through three stages: early stage, mild cognitive impairment (MCI) (middle stage), and dementia. Early diagnosis of Alzheimer’s disease is crucial and can improve survival rates among patients. Traditional methods for diagnosing AD through regular checkups and manual examinations are challenging. Advances in computer-aided diagnosis systems (CADs) have led to the development of various artificial intelligence and deep learning-based methods for rapid AD detection. This survey aims to explore the different modalities, feature extraction methods, datasets, machine learning techniques, and validation methods used in AD detection. We reviewed 116 relevant papers from repositories including Elsevier (45), IEEE (25), Springer (19), Wiley (6), PLOS One (5), MDPI (3), World Scientific (3), Frontiers (3), PeerJ (2), Hindawi (2), IO Press (1), and other multiple sources (2). The review is presented in tables for ease of reference, allowing readers to quickly grasp the key findings of each study. Additionally, this review addresses the challenges in the current literature and emphasizes the importance of interpretability and explainability in understanding deep learning model predictions. The primary goal is to assess existing techniques for AD identification and highlight obstacles to guide future research.