Cardiac diseases are recognized as the leading cause of mortality, hospitalization, and medical prescription globally. The gold standard for the treatment of coronary artery stenosis is the percutaneous cardiac intervention that is performed under live X-ray imaging. Substantial clinical evidence shows that the surgeon and staff are prone to serious health problems due to X-ray exposure and occupational hazards. Telerobotic vascular intervention systems with a master-slave architecture reduced the X-ray exposure and enhanced the clinical outcomes; however, the loss of haptic feedback during surgery has been the main limitation of such systems. This paper is a review of the state of the art for haptic telerobotic cardiovascular interventions. A survey on the literature published between 2000 and 2019 was performed. Results of the survey were screened based on their relevance to this paper. Also, the leading research disciplines were identified based on the results of the survey. Furthermore, different approaches for sensor-based and model-based haptic telerobotic cardiovascular intervention, haptic rendering and actuation, and the pertinent methods were critically reviewed and compared. In the end, the current limitations of the state of the art, unexplored research areas as well as the future perspective of the research on this technology were laid out.