Auscultation plays an important role in the clinic, and the research community has been exploring machine learning (ML) to enable remote and automatic auscultation for respiratory condition screening via sounds. To give the big picture of what is going on in this field, in this narrative review, we describe publicly available audio databases that can be used for experiments, illustrate the developed ML methods proposed to date, and flag some under-considered issues which still need attention. Compared to existing surveys on the topic, we cover the latest literature, especially those audio-based COVID-19 detection studies which have gained extensive attention in the last two years. This work can help to facilitate the application of artificial intelligence in the respiratory auscultation field.