The structural, chemical, and electronic characteristics of graphene grown by thermal decomposition of a singlecrystal SiC substrate in Ar atmosphere are presented. It is shown that this technology allows the creation of high-quality monolayer graphene films with a small fraction of bilayer graphene inclusions. The performance of graphene on SiC as a gas sensor or a biosensor was tested. The sensitivity of gas sensors to NO2 on the order of 1 ppb and that of biosensors to fluorescein with concentration on the order of 1 ng/mL and to bovine serum albumin-fluorescein conjugate with concentration on the order of 1 ng/mL were determined.