Heart sound auscultation has been demonstrated to be beneficial in clinical usage for early screening of cardiovascular diseases. Due to the high requirement of well-trained professionals for auscultation, automatic auscultation benefiting from signal processing and machine learning can help auxiliary diagnosis and reduce the burdens of training professional clinicians. Nevertheless, classic machine learning is limited to performance improvement in the era of big data. Deep learning has achieved better performance than classic machine learning in many research fields, as it employs more complex model architectures with stronger capability of extracting effective representations. Deep learning has been successfully applied to heart sound analysis in the past years. As most review works about heart sound analysis were given before 2017, the present survey is the first to work on a comprehensive overview to summarise papers on heart sound analysis with deep learning in the past six years 2017--2022. We introduce 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.