Medical images are increasingly being presented on soft-copy displays such as CRTs but without, in our opinion, consistent visualization of the medical image data. Reaction to earlier calls for implementing a display standard for medical images has been slow. This has prompted us to write a tutorial which we hope will accelerate the acceptance of standardized image presentation on soft-copy displays in electronic radiology. The types of medical images and their visualization (luminance tone scale and dynamic range) are discussed. The impact of ambient lighting on the observed tone scale is also analyzed. Since the human observer is the detector of medical images, we review the critical parameters that characterize the human visual system, HVS [H. Blume, S. Daly, and E. Muka, 'Presentation of Medical Images on CRT Displays -- A Renewed Proposal for a Display Function Standard,' Proc. SPIE Vol. 1897 Image Capture, Formatting, and Display, pp. 215 - 231, (1993)]. We provide additional information regarding the proposed mathematical representation of the HVS `display function' and threshold contrast modulation and show how they are related. We discuss the differences between the desired visualization of a set of medical data versus the display function of a soft-copy display such as a CRT. To facilitate the objective that images can be consistently rendered, we repeat our call for a standardized display function for soft- copy displays and believe that is should be based on the HVS. We discuss which medical image data should be perceptually linearized throughout the medical data dynamic range. These points are demonstrated using typical CT images and digitized projection radiographs presented with different gray scales.