Adaptive Signal Processing (ASP) algorithms have revolutionized remote health monitoring systems through integration into the biomedical device. With the pressure on global healthcare systems to deliver scalable, patient-centric monitoring frameworks, ASP algorithms can help transform how healthcare services are provided now and in the future. The algorithms adapt to different physiological conditions, suppress noise while extracting critical features in real-time, and improve the accuracy and reliability of biomedical diagnostics. In this paper, current advancements and applications of ASP within remote biomedical monitoring are presented, and several adaptive filtering techniques (Least Mean Square (LMS), Recursive Least Squares (RLS), and Kalman filters) are described. Wearable biosensors, IoT, and ASP work in tandem to augment the capabilities of e-health systems to process physiological data continuously and in real time. A number of case studies (including ECG monitoring and EEG-based brain-computer interfaces) are described, which demonstrate the practical utility of ASP in diagnosing cardiovascular anomalies, detecting epileptic seizures, and monitoring respiratory irregularities. This paper also assesses algorithmic performance in terms of convergence rate, efficiency through computational cost, and signal-to-noise ratio (SNR). These discussions are supported by a literature review including recent results in medical engineering and signal processing. An experimental setup is proposed by the methodology section that uses simulated biomedical signals, the prototyping of hardware using Arduino, and MATLAB-based signal analysis. The results demonstrate a significant improvement in noise suppression and anomaly detection compared with traditional signal processing techniques. These findings highlight the strong potential of adaptive signal processing (ASP) for applications in telemedicine and personalized medicine.