Graphene growth by thermal decomposition of silicon carbide (SiC) is a technique that produces wafer-scale, single-orientation graphene on an insulating substrate. It is often referred to as epigraphene, and has been thought to be suitable for electronics applications. In particular, high-frequency devices for communication technology or large quantum Hall plateau for metrology applications using epigraphene are expected, which require high carrier mobility. However, the carrier mobility of as-grown epigraphene exhibit the relatively low values of about 1000 cm2/Vs. Fortunately, we can hope to improve this situation by controlling the electronic state of epigraphene by modifying the surface and interface structures. In this paper, the mobility of epigraphene and the factors that govern it will be described, followed by a discussion of attempts that have been made to improve mobility in this field. These understandings are of great importance for next-generation high-speed electronics using graphene.