Phase-change materials (PCMs) and metal-insulator transition (MIT) materials have the unique feature of changing their material phase through external excitations such as conductive heating, optical stimulation, or the application of electric or magnetic fields, which, in turn, results in changes to their electrical and optical properties. This feature can find applications in many fields, particularly in reconfigurable electrical and optical structures. Among these applications, the reconfigurable intelligent surface (RIS) has emerged as a promising platform for both wireless RF applications as well as optical ones. This paper reviews the current, state-of-the-art PCMs within the context of RIS, their material properties, their performance metrics, some applications found in the literature, and how they can impact the future of RIS.