The Internet of Things (IoT) is a rapidly expanding network of interconnected things that use embedded sensors to gather and share data in real‐time. IoT technologies have given rise to many networking applications in our everyday life such as smart homes, smart cities, smart transport, and so forth. Smart healthcare is one such application that has been revolutionized by the IoT, introducing a new branch of IoT known as the Internet of Medical Things (IoMT). IoMT encompasses an entire ecosystem consisting of smart wearable, implantable sensing equipment's or devices, transmitters that are critical for monitoring the patients remotely and continuing the real‐time and has opened the door to new innovative smart healthcare approaches while improving patient care outcomes. IoMT wearable and embedded sensing devices are commonly utilized in smart healthcare to capture medical data and transmit the medical data in a communication network stored in the cloud. The large volume of data generated and transmitted by these IoMT devices is rising at an exponential rate, resulting in an increase in security and privacy vulnerabilities of healthcare data. To ensure the Confidentiality and integrity of the IoMT devices and the sensitive medical data, there should be proper security and privacy measures such as access control, passwords, multifactor authentication, and encryption of data generated, transmitted, or processed in the IoMT framework. In this paper, we identified the internet of things and its applications in smart healthcare systems. Additionally, the paper focuses on the architecture of IoMT, and several challenges, including the IoMT security and privacy requirements, and attack taxonomy. Furthermore, the paper thoroughly investigates both cryptographic and non‐cryptographic based security and privacy‐enhancing techniques for IoMT or healthcare systems with particular emphasis on advancements in key areas such as Homomorphic Encryption, Differential Privacy, and Federated Learning.