Medical cyber-physical systems (MCPS) are lifecritical, context-aware, networked systems of medical devices. These systems are increasingly used in hospitals to provide highquality continuous care for patients. The need to design complex MCPS that are both safe and effective has presented numerous challenges, including achieving high assurance in system software, intoperability, context-aware intelligence, autonomy, security and privacy, and device certifiability. In this paper, we discuss these challenges in developing MCPS, some of our work in addressing them, and several open research issues