Cardiovascular diseases (CVDs) persist as the leading cause of global mortality, presenting a formidable challenge to healthcare systems worldwide. While clinical guidelines provide a framework for diagnosis and management, the integration of Machine Learning (ML) offers a paradigm shift towards data-driven, personalized cardiology. This paper investigates the real-world implementation of ML algorithms for heart disease prediction, stratification, and management. It critically examines the complete pipeline, from data acquisition and preprocessing to the deployment and operationalization of models within clinical workflows. A significant focus is placed on the practical challenges encountered, including data heterogeneity, model interpretability, and integration with existing electronic health record (EHR) systems. Furthermore, the paper proposes and discusses contemporary solutions to these challenges, such as federated learning for privacy-preserving data analysis, explainable AI (XAI) techniques for building clinician trust, and MLOps practices for sustainable model lifecycle management. By synthesizing recent advancements and pragmatic implementation strategies, this work aims to bridge the gap between theoretical model performance and tangible clinical impact, outlining a pathway for the effective adoption of ML in combating heart disease.