Teleradiology allows medical images to be transmitted over electronic networks for clinical interpretation and for improved healthcare access, delivery, and standards. Although such remote transmission of the images is raising various new and complex legal and ethical issues, including image retention and fraud, privacy, malpractice liability, etc., considerations of the security measures used in teleradiology remain unchanged. Addressing this problem naturally warrants investigations on the security measures for their relative functional limitations and for the scope of considering them further. In this paper, starting with various security and privacy standards, the security requirements of medical images as well as expected threats in teleradiology are reviewed. This will make it possible to determine the limitations of the conventional measures used against the expected threats. Furthermore, we thoroughly study the utilization of digital watermarking for teleradiology. Following the key attributes and roles of various watermarking parameters, justification for watermarking over conventional security measures is made in terms of their various objectives, properties, and requirements. We also outline the main objectives of medical image watermarking for teleradiology and provide recommendations on suitable watermarking techniques and their characterization. Finally, concluding remarks and directions for future research are presented.