Cardiovascular diseases, more commonly known as heart diseases, are deadly and early mortality diseases that are increasingly being diagnosed in youth and middle-aged individuals, regardless of age or co-morbidities. Due to the sudden rise in heart-related disease after COVID-19, there is a great need for technology that helps in its prediction and analysis. Data mining and machine learning algorithms help clinicians in early-stage prediction, decision-making, and disease diagnosis. Several supervised and unsupervised data mining and machine learning algorithms were developed for the prediction and analysis of heart disease. In this paper, we mainly focus on the datasets available for heart disease prediction as well as merits and demerits of the different algorithms developed so far. The performance of these algorithms is measured by the computation of the accuracy. It has been observed that the algorithm with hybrid approach gives better results in terms of accuracy. Further, the issues related to heart disease datasets, i.e., missing values, extraneous feature sets, data redundancy, class imbalance, data uncertainty, etc., are also discussed in detail. This study will help researchers with the development of efficient and accurate algorithms for heart disease prediction and analysis.