Vitreoretinal surgery represents a medical procedure whose tasks exist on the edge of human capability, given the relative scale of possible human hand movements, and afflicted areas on the retina. Performing vitreoretinal surgery using teleoperated robots, as opposed to manually, can potentially greatly reduce the difficulty level and required skill, and minimize the risk for the patient. However, the method employed by existing microsurgery robots for computing the remote centre of motion (RCM) of their surgical tool depends on a spherical eye model which is insufficiently accurate. In this thesis, a safety concern associated with inaccurate RCM placement is shown. A computer vision-based system is proposed which can provide an accurate, model-free RCM placement, as well as enable automatic microscope positioning. A camera is added to a microsurgery robot and the video feed is segmented to locate the iris and trocars in real time in 2-D using a convolutional neural network (CNN). The computed trocar positions are used in tandem with information provided by the robot’s encoders to place the 3-D position of the slave robot’s RCM. The iris position can be used to align the iris with the microscope automatically, to provide the view of the workspace inside the eye. The system’s accuracy is validated in a dry-lab experiment.