Artificial intelligence (AI) will transform the sphere of anesthesiology by helping physicians make more informed decisions using the data before, during, and after surgery. In this article, the author goes into detail on the possible uses of AI in the anesthesia practice, such as anesthesia depth monitoring in real-time, predicting hemodynamic instability, better drug delivery systems, and predicting post-surgery difficulty. The comparative analysis of popular machine learning (ML) and deep learning (DL) techniques in different fields is performed. We show the practical approach of applying ensemble models, which include gradient boosting, stacking, and blending classifiers, to make predictions of intraoperative hypotension based on the VitalDB data. Optimum AUC and F1-scores are thereby obtained. SHAP (SHapley Additive exPlanations) helps us to find meaningful physiological features, which makes our work easy to understand. The article addresses the ethical, legal, and practical challenges involved in the application of AI in healthcare settings, such as data protection of patient information, ease of use, and electronic health systems integration. Lastly, we mention the role of federated and multimodal AI models in the future of providing more personalized anesthesia. The work will be of great value to doctors, researchers, and programmers who want to apply AI in anesthesia processes in a safe and effective manner.