It is well known that graphene, which brought the 2010 Noble Prize in physics to Russian scientists Andre Geim and Konstantin Novoselov, exists as two-dimensional carbon layers. The possible range of graphene applications includes development of field-effect transistors for digital and analog electronics, nanoelectromechanical systems, quantum dots, cold cathodes, supersapacitor, gas sensors, and nearly transparent electrodes and coatings. The possibility of using graphene for hydrogen storage and the manufacture of composite materials is also being studied. Being a two-dimensional material, graphene provides ultimate one-dimensional miniaturization and is a convenient basis for manufacture of different nanoelectronic, nanomechanical and nanochemical devices by lithographic methods. The graphene-based device which is closest to being successfully realized for practical application is the gas sensor. The use of graphene makes it possible to achieve a sensitivity exceeding that of all other materials, less than 1ppb. This device combines the comparative simplicity of manufacture with a wide spectrum of possible applications. It should also be mentioned that the structure of the gas sensor actually reproduces the structure of the field-effect transistor. Thus, the gas sensor can be considered the first stage in the development of intricate transistor electronics based on graphene. The paper briefly reviews growth experiments and studies of graphene films on silicon carbide (SiC) and the development of prototype gas sensors based on this material.