The development of autonomous vehicles, both ground and airborne, for hospitals and clinical settings is an extremely interesting topic that has developed rapidly in recent years. Given their significant potential to improve operational efficiency and safety protocols, these devices are gradually gaining an important place in the healthcare industry. This is true for both in-hospital and out-of-hospital functions. The integration of autonomous vehicles into these environments will greatly increase operational efficiency and enrich the experience for both medical staff and patients. This document provides an updated and comprehensive overview of the current state-of-the-art in the development of autonomous vehicles for the healthcare sector. Particular emphasis is placed on design, functionality, and level of autonomy. The review is organized on two levels: a prospective review highlights the main trends in the design and application of autonomous vehicles, and an analytical review performs an in-depth analysis of the main aspects of the technical solutions developed and implemented in the scientific research reviewed. The results are presented in a schematic approach.