Heart sound auscultation has been applied in clinical usage for early screening of cardiovascular diseases. Due to the high demand for auscultation expertise, automatic auscultation can help with auxiliary diagnosis and reduce the burden of training professional clinicians. Nevertheless, there is a limit to classic machine learning's performance improvement in the era of big data. Deep learning has outperformed classic machine learning in many research fields, as it employs more complex model architectures with a stronger capability of extracting effective representations. Moreover, it has been successfully applied to heart sound analysis in the past years. As most review works about heart sound analysis were carried out before 2017, the present survey is the first to work on a comprehensive overview to summarise papers on heart sound analysis with deep learning published in 2017--2022. This work introduces both classic machine learning and deep learning for comparison, and further offer insights about the advances and future research directions in deep learning for heart sound analysis. Our repository is publicly available at \url{https://github.com/zhaoren91/awesome-heart-sound-analysis}.
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