Health monitoring and its related technologies is an attractive research area. The electrocardiogram (ECG) has always been a popular measurement scheme to assess and diagnose cardiovascular diseases (CVDs). The number of ECG monitoring systems in the literature is expanding exponentially. Hence, it is very hard for researchers and healthcare experts to choose, compare, and evaluate systems that serve their needs and fulfill the monitoring requirements. This accentuates the need for a verified reference guiding the design, classification, and analysis of ECG monitoring systems, serving both researchers and professionals in the field. In this paper, we propose a comprehensive, expert-verified taxonomy of ECG monitoring systems and conduct an extensive, systematic review of the literature. This provides evidence-based support for critically understanding ECG monitoring systems’ components, contexts, features, and challenges. Hence, a generic architectural model for ECG monitoring systems is proposed, an extensive analysis of ECG monitoring systems’ value chain is conducted, and a thorough review of the relevant literature, classified against the experts’ taxonomy, is presented, highlighting challenges and current trends. Finally, we identify key challenges and emphasize the importance of smart monitoring systems that leverage new technologies, including deep learning, artificial intelligence (AI), Big Data and Internet of Things (IoT), to provide efficient, cost-aware, and fully connected monitoring systems.