This comprehensive review explores data-driven methodologies that facilitate the prognostics and health management (PHM) of centrifugal pumps (CPs) while utilizing both vibration and non-vibration sensor data. This review investigates common fault types in CPs, while placing a specific emphasis on artificial intelligence (AI) approaches, including machine learning (ML) and deep learning (DL) techniques, for fault diagnosis and prognosis. A key innovation of this review is its in-depth analysis of cutting-edge methods, such as adaptive thresholding, hybrid models, and advanced neural network architectures, aimed at accurately predicting the remaining useful life (RUL) of CPs under varying operational conditions. This review also addresses the limitations and challenges of the current AI-driven methodologies, offering insights into potential solutions. By synthesizing these methodologies and presenting practical applications through case studies, this review provides a forward-looking perspective to empower industry professionals and researchers with effective strategies to ensure the reliability and efficiency of centrifugal pumps. These findings could contribute to optimizing industrial processes and advancing health management strategies for critical components.