This article presents a systematic review of recent advancements in telemedicine architectures for continuous monitoring, providing a comprehensive overview of the evolving software engineering practices underpinning these systems. The review aims to illuminate the critical role of telemedicine in delivering healthcare services, especially during global health crises, and to emphasize the importance of effectiveness, security, interoperability, and scalability in these systems. A systematic review methodology was employed, adhering to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses framework. As the primary research method, the PubMed, IEEE Xplore, and Scopus databases were searched to identify articles relevant to telemedicine architectures for continuous monitoring. Seventeen articles were selected for analysis, and a methodical approach was employed to investigate and synthesize the findings. The review identified a notable trend towards the integration of emerging technologies into telemedicine architectures. Key areas of focus include interoperability, security, and scalability. Innovations such as cognitive radio technology, behavior-based control architectures, Health Level Seven International (HL7) Fast Healthcare Interoperability Resources (FHIR) standards, cloud computing, decentralized systems, and blockchain technology are addressing challenges in remote healthcare delivery and continuous monitoring. This review highlights major advancements in telemedicine architectures, emphasizing the integration of advanced technologies to improve interoperability, security, and scalability. The findings underscore the successful application of cognitive radio technology, behavior-based control, HL7 FHIR standards, cloud computing, decentralized systems, and blockchain in advancing remote healthcare delivery.