Early diagnosis of heart disease is a crucial area of medical study, and the application of machine learning (ML) and deep learning (DL) techniques in this field has yielded encouraging results. The identification of cardiac problems using ML and DL approaches has been the subject of earlier research, which is presented in this study, along with a thorough survey and comparative analysis. A broad variety of supervised learning algorithms, such as decision trees (DT), support vector machines (SVM), random forest (RF), Naive Bayes (NB), k-nearest neighbors (KNN), and DL methods, such as convolutional neural networks (CNN), artificial neural networks (ANN), recurrent neural networks (RNN), and long short-term memory (LSTM), were explored in this study. Their advantages and disadvantages are also examined. The study also analyzes the difficulties in detecting cardiac illness, including data accuracy, interpretability, generalizability, and possible biases, and offers insights into potential future research directions.