Cardiac health of the human heart is an intriguing issue for many decades as cardiovascular diseases (CVDs) are the leading cause of death worldwide. Electrocardiogram (ECG) signal is a powerful complete non-invasive tool for analyzing cardiac health. ECG signal is the primary choice of various health practitioners to determine vital information about the human heart. In the literature, the ECG signals are studied to diagnose and detect heart abnormalities such as enlargement of a heart chamber, detect cardiovascular diseases, detect ischemia, measure heart rate, biometric identification, and name a few. ECG signal being feeble suffers from the different kinds of noises, which might damage the ECG signal's morphological features, leading to wrong information and improper treatment. Removal of the noises from the ECG signal is an essential part of ECG signal processing. The denoised ECG signal facilitates the correct detection of the morphological features, which provides appropriate information about the cardiac health of the human heart. Detection of morphological features typically includes detecting QRS complex, R peak, and other ECG signal characteristics. These detected features are used to predict CVDs and other heart abnormalities. Earlier and accurate detection of CVDs involves two main steps: denoising and detection of a morphological feature. The increasing mortality rate due to CVDs compelled researchers to invent efficient computational techniques that automatically detect abnormalities in the heart. In the past few decades, various researchers have been proposed many computational methods to denoise and detect the ECG signal. This paper presents a comparative study of various existing state-of-the-art techniques used to analyze the ECG signal. Various noises influence the performance of the existing computational methods; hence, a summary of the different noises presented in the ECG signal is also included. The advantages and drawbacks of each method for ECG signal denoising and detection are discussed briefly. The efficiency of denoising and detection techniques was evaluated by testing the proposed algorithms using different standard databases like MIT-BIH, AHA, PTB, MIT-BIH noise stress test, Apnea-ECG. Details of these standard databases are provided in the paper. The performance of existing ECG signal denoising and detection algorithms is compared using parameters like signal-to-noise ratio improvement, percentage root mean square difference, root mean square error, sensitivity, positive predictivity, error, and accuracy. Finally, the challenges and gaps of the existing state-of-the-art techniques to analyze the ECG signal for automatic detection of CVDs are discussed.