—Bilateral teleoperation systems with haptic feedback allow human users to interact with objects or perform complex tasks in remote or inaccessible environments. Communication delays in teleoperation systems jeopardize system stability and transparency, leading to degraded system performance and poor user experience. In this paper, we provide a survey of the model-mediated teleoperation (MMT) approach, which has been developed to guarantee both system stability and transparency in the presence of arbitrary communication delays. This survey focuses on two major parts: 1) the historical development of the MMT approach from the late 1980s to the present and 2) the main challenges facing the design of a reliable MMT system. Along with the discussion of the MMT challenges and the proposed solutions, a series of experiments have been conducted to compare the performance between the existing techniques and to supply data that were missing in previous studies on the MMT approach.