Understanding the physics and technology of Schottky contacts to Silicon Carbide is important, for both academic and industrial researchers. In fact, the rectifying contact is a tool for studying carrier transport at metal/semiconductor interfaces, as well as forming the main building block of the Schottky Barrier Diode. In this chapter, the physics of metal/SiC rectifying contacts and the technology of 4H-SiC Schottky diodes are reviewed, presenting a survey of relevant results on this topic, from fundamental concepts of Schottky barriers, to practical information for real device fabrication. Selected examples of 4H-SiC Schottky diodes applications are also briefly discussed.