There is a rise in the level of e-commerce websites, and so business has an increased need to have clever, user-friendly search and personalization options. This paper reviews search and personalization in e-commerce using AI/ML, and integrates the outcomes of both early pioneering and recent studies on search and personalization in e-commerce. Based on the empirical evidence, the performance of deep learning and hybrid models beats the traditional approaches in terms of such indicators of success as the hit rate, NDCG, and conversion rates. It reports on the current research on ongoing issues: explainability of models, data privacy, scalability, and multimodal data integration, as well as possible directions of further research, such as developments in privacy-preserving models, real-time adaptation, and research on ethical AI. The paper gives a general picture of research in the field and locates the main opportunities for further development in the sphere of e-commerce personalization.