With modern medicine and healthcare services improving in leaps and bounds, the integration of telemedicine has helped in expanding these specialised healthcare services to remote locations. Healthcare telerobotic systems form a component of telemedicine, which allows medical intervention from a distance. It has been nearly 40 years since a robotic technology, PUMA 560, was introduced to perform a stereotaxic biopsy in the brain. The use of telemanipulators for remote surgical procedures began around 1995, with the Aesop, the Zeus, and the da Vinci robotic surgery systems. Since then, the utilisation of robots has steadily increased in diverse healthcare disciplines, from clinical diagnosis to telesurgery. The telemanipulator system functions in a master–slave protocol mode, with the doctor operating the master system, aided by audio-visual and haptic feedback. Based on the control commands from the master, the slave system, a remote manipulator, interacts directly with the patient. It eliminates the requirement for the doctor to be physically present in the spatial vicinity of the patient by virtually bringing expert-guided medical services to them. Post the Covid-19 pandemic, an exponential surge in the utilisation of telerobotic systems has been observed. This study aims to present an organised review of the state-of-the-art telemanipulators used for remote diagnostic procedures and surgeries, highlighting their challenges and scope for future research and development.