Substrate selection presents particular challenges for the production of high-quality high-temperature superconducting (HTS) thin films suitable for applications. Because the substrate is generally a passive component, it is often ignored and assumed to have a negligible effect on the structure residing on top of it. There is also a technological motivation to use substrates that conventional wisdom would argue are unlikely to support high-quality HTS films. These facts have led to rediscovery of many of the fundamental issues governing the role of the substrate in determining the properties of the thin film(s) it supports. For this reason, the study of issues in substrate selection for HTS materials presents a microcosm for substrate selection more generally. We consider the major issues governing the role of the substrate in HTS thin-film technology and discuss many of the material classes and specific materials that have been studied for their suitability as substrates for HTS films.