Alzheimer’s disease (AD) is a progressive disease that damages memory as well as other essential brain functions. The emerging discipline of artificial intelligence (AI), especially machine learning (ML) and deep learning (DL), has the potential to improve the ability of early detection and understanding of AD. Our review gives a synopsis of data from recent studies as we look into the diverse ML and DL algorithms used with neuroimaging and genetic data to evaluate their performance and find limitations. Diagnostic accuracies of upto 99 per cent were achieved by Convolutional Neural Networks (CNN) on multimodal datasets. SHapley additive exPlanations (SHAP) and local interpretable model-agnostic explanations (LIME) produced accuracy of 97 per cent when combined with support vector machines (SVM). In methylation-based diagnostics, ensemble models achieved an area under curve (AUC) value of 0.998. In addition, we recommend future research directions to address the issues found. This comprehensive analysis seeks to give in-depth information for researchers and practitioners interested in using artificial intelligence for AD diagnosis and prognosis. Model interpretability and diagnostic accuracy have been significantly enhanced by the integration of neuroimaging, genetics as well as epigenetic data with explainable AI (XAI) techniques. It will be important that addressing remaining challenges like data heterogeneity and computational scalability are done for translating these improvements into real-world clinical applications and patient outcomes.