The internet of medical things has been developed to facilitate remote monitoring of the patients as well as the elderly. Unfortunately, the communication between the remote patients and the medical doctors is the open wireless channels. Therefore, the data transmitted can be eavesdropped, intercepted, replayed or modified. This poses serious challenges to patient privacy as well as endangering patient life. To curb this, numerous schemes have been put forward by various researchers over the recent past. In this paper, we provide an extensive review of these schemes in an effort to identify any gaps. Consequently, we show that the current security and privacy preservation schemes have many challenges that render the communication process insecure or inefficient. As such, we offer some suggestions for the requirements of an ideal security technique that will not only be efficient but also provably secure.