Silicon carbide (4H-SiC) Schottky diodes have reached a mature level of technology and are today essential elements in many applications of power electronics. In this context, the study of Schottky barriers on 4H-SiC is of primary importance, since a deeper understanding of the metal/4H-SiC interface is the prerequisite to improving the electrical properties of these devices. To this aim, over the last three decades, many efforts have been devoted to developing the technology for 4H-SiC-based Schottky diodes. In this review paper, after a brief introduction to the fundamental properties and electrical characterization of metal/4H-SiC Schottky barriers, an overview of the best-established materials and processing for the fabrication of Schottky contacts to 4H-SiC is given. Afterwards, besides the consolidated approaches, a variety of nonconventional methods proposed in literature to control the Schottky barrier properties for specific applications is presented. Besides the possibility of gaining insight into the physical characteristics of the Schottky contact, this subject is of particular interest for the device makers, in order to develop a new class of Schottky diodes with superior characteristics.