There is a vast body of literature concerning the capture, storing, transmission and display of High Dynamic Range (HDR) imaging. Nevertheless, there are few works that try to address the problem of getting HDR on mobile devices. Their hardware limitations, such as processing power, storage space, graphics capabilities and screen characteristics, transform that problem in a big challenge. However, since more and more HDR content is being produced and given that in a few years it can become a standard, it is necessary to provide the means to visualize HDR images and video on mobile devices. The main goal of this paper is to present a survey on HDR visualization approaches and techniques developed specifically for mobile devices. To understand what are the main challenges that need to be addressed in order to visualize HDR on mobile devices, an overview of their main characteristics is given. The very low dynamic range of most of mobile devices' displays implies that a tone mapping operator (TMO) must be applied in order to visualize the HDR content. The current status of the research on TMO will be presented and analyzed, a special attention will be given to the ones that were developed taking in account the limited characteristics of the mobile devices' displays. Another important issue is visualization quality assessment, meaning visualize HDR content without losing the main characteristics of the original HDR content. Thus, evaluation studies of HDR content visualization on mobile devices will be presented and their results analyzed.