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Distribution shifts pose a major challenge for artificial intelligence (AI) deployed in healthcare systems, as models trained on historical or controlled datasets often perform poorly in evolving clinical environments. This narrative review synthesizes current approaches for detecting, adapting to, and classifying failures associated with distribution shifts in AI-driven healthcare analytics. Sources of shift—including changes in patient demographics, imaging protocols, institutional practices, and temporal dynamics—can significantly affect clinical decision support, predictive modeling, and operational analytics.We examine detection strategies based on statistical divergence monitoring and discuss adaptation methods such as domain adaptation and privacy-preserving learning approaches designed to maintain model performance across institutions. Failure modes are organized into core categories, including covariate shift, label shift, and concept drift, with particular attention to healthcare-specific risks such as bias amplification and breakdowns in continuous monitoring systems.From a systems perspective, the review highlights the importance of integrating shift detection with clinical analytics pipelines, governance mechanisms, and explainable AI tools to support safe deployment. We propose an interpretive framework linking data ingestion, model inference, intervention feedback, and oversight processes within healthcare infrastructures. Despite advances in detection and adaptation techniques, real-time operational deployment and standardized failure classification remain significant gaps. Strengthening these areas is essential for developing resilient AI systems capable of maintaining reliability in dynamic healthcare environments.