The automated classification of heart sounds plays a significant role in the diagnosis of cardiovascular diseases (CVDs). With the recent introduction of medical big data and artificial intelligence technology, there has been an increased focus on the development of deep learning approaches for heart sound classification. However, despite significant achievements in this field, there are still limitations due to insufficient data, inefficient training, and the unavailability of effective models. With the aim of improving the accuracy of heart sounds classification, an in-depth systematic review and an analysis of existing deep learning methods were performed in the present study, with an emphasis on the convolutional neural network (CNN) and recurrent neural network (RNN) methods developed over the last five years. This paper also discusses the challenges and expected future trends in the application of deep learning to heart sounds classification with the objective of providing an essential reference for further study.