This review is devoted to one of the most promising two-dimensional (2D) materials, graphene. Graphene can be prepared by different methods and the one discussed here is fabricated by the thermal decomposition of SiC. The aim of the paper is to overview the fabrication aspects, growth mechanisms, and structural and electronic properties of graphene on SiC and the means of their assessment. Starting from historical aspects, it is shown that the most optimal conditions resulting in a large area of one ML graphene comprise high temperature and argon ambience, which allow better controllability and reproducibility of the graphene quality. Elemental intercalation as a means to overcome the problem of substrate influence on graphene carrier mobility has been described. The most common characterization techniques used are low-energy electron microscopy (LEEM), angle-resolved photoelectron spectroscopy (ARPES), Raman spectroscopy, atomic force microscopy (AFM) in different modes, Hall measurements, etc. The main results point to the applicability of graphene on SiC in quantum metrology, and the understanding of new physics and growth phenomena of 2D materials and devices.