In this review paper, an overview of the application of n-type 4H-SiC Schottky barrier diodes (SBDs) as radiation detectors is given. We have chosen 4H-SiC SBDs among other semiconductor devices such as PiN diodes or metal-oxide-semiconductor (MOS) structures, as significant progress has been achieved in radiation detection applications of SBDs in the last decade. Here, we present the recent advances at all key stages in the application of 4H-SiC SBDs as radiation detectors, namely: SBDs fabrication, electrical characterization of SBDs, and their radiation response. The main achievements are highlighted, and the main challenges are discussed.