Electrocardiogram (ECG) signals are vital diagnostic tools used widely in clinical and research settings to monitor cardiac health. However, the quality and interpretability of ECG signals are often compromised by various types of noise and artifacts, such as power line interference, baseline wander, and motion artifacts. Effective removal of these unwanted disturbances is crucial to ensure accurate diagnosis and reliable analysis. This review paper provides a comprehensive overview of digital filtering methods employed in ECG signal processing, emphasizing the development and application of Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) filters. The study discusses the characteristics, advantages, and limitations of common digital filters such as Butterworth, Chebyshev, and Elliptic filters, highlighting their roles in attenuating noise while preserving essential morphological features of the ECG waveform. It underscores the trend toward utilizing IIR filters due to their efficiency in achieving steep frequency responses with fewer coefficients, thus reducing computational load and enabling real-time processing. Additionally, the review examines the integration of digital filters within matrix systems like MATLAB, illustrating their widespread adoption for ECG data analysis. Critical challenges encountered in ECG filtering are addressed, including the trade-off between filter complexity and signal integrity, as well as potential artifacts introduced by filtering techniques. Furthermore, the paper explores emerging digital filtering algorithms and their potential enhancements in noise reduction, along with future research directions involving internet-based alarm systems and advanced adaptive filtering solutions for improved heart attack prevention and cardiac diagnostics. This review concludes by emphasizing the importance of continuous innovation in filter design and implementation to enhance the accuracy, reliability, and efficiency of ECG signal processing in biomedical applications.