<p>In recent years, as an emerging technology, Cyber-Physical System (CPS) has received significant research interest among the research community due to their various applications in several domains including cognitive healthcare, smart cities, smart grids, intelligent manufacturing, and climate-smart agriculture, among others. In particular, Medical Cyber-Physical Systems (MCPSs) are a sort of CPS that are specially built for use in the healthcare domain. MCPSs are important to the healthcare industry as they are life- critical, however they are prone to data breaches and cyber threats. Therefore, security and privacy are the primary issues in MCPS. Motivated by the advantages, applications, and challenges of MCPS, in this work, we discuss various security and privacy issues of MCPS. We have explored the fundamentals of CPS and MCPS along with the framework of MCPS. Subsequently, various attacks, vulnerabilities, and security risks in MCPS are inspected. This work also presents the classification of attacks in MCPS based on intention, goal, and impact, in addition to Artificial Intelligence (AI) based attacks in MCPS. Moreover, we have investigated various approaches to ensure security and privacy in MCPS, which covers several security and privacy standards along with the various security and privacy frameworks in MCPS. Finally, the key research perspectives and directions are discussed herein. Hence, this work provides readers with the latest progress and a thorough understanding of the key features and technological approaches of MCPS with respect to security and privacy.</p>