Recent years have seen a rapid increase in digital medicine research in an attempt to transform traditional healthcare systems to their modern, intelligent, and versatile equivalents that are adequately equipped to tackle contemporary challenges. This has led to a wave of applications that utilise AI technologies; first and foremost in the fields of medical imaging, but also in the use of wearables and other intelligent sensors. In comparison, computer audition can be seen to be lagging behind, at least in terms of commercial interest. Yet, audition has long been a staple assistant for medical practitioners, with the stethoscope being the quintessential sign of doctors around the world. Transforming this traditional technology with the use of AI entails a set of unique challenges. We categorise the advances needed in four key pillars: Hear, corresponding to the cornerstone technologies needed to analyse auditory signals in real-life conditions; Earlier, for the advances needed in computational and data efficiency; Attentively, for accounting to individual differences and handling the longitudinal nature of medical data; and, finally, Responsibly, for ensuring compliance to the ethical standards accorded to the field of medicine.