Medicine’s ability to quickly respond to challenges raises questions from researchers, practitioners, and society as a whole. Our task in this study was to identify key and atypical current factors influencing the development of medicine and to predict the development of medicine in the short, medium, and long term. To implement our study, we selected 22 medical experts and applied the three-level Delphi method. The current trends caused by COVID-19 have a short-term impact, but they will launch other drivers that will transform the healthcare industry. Well-being technologies, data-informed personalization, and climate change will become key drivers for the development of medicine over the period of 1–50 years. Expert opinion is divided about the future of mass availability of advanced medical treatment and sustainable development of healthcare.