4H-SiC single photon counting avalanche photodiodes (SPADs) are prior devices for weak ultraviolet (UV) signal detection with the advantages of small size, low leakage current, high avalanche multiplication gain, and high quantum efficiency, which benefit from the large bandgap energy, high carrier drift velocity and excellent physical stability of 4H-SiC semiconductor material. UV detectors are widely used in many key applications, such as missile plume detection, corona discharge, UV astronomy, and biological and chemical agent detection. In this paper, we will describe basic concepts and review recent results on device design, process development, and basic characterizations of 4H-SiC avalanche photodiodes. Several promising device structures and uniformity of avalanche multiplication are discussed, which are important for achieving high performance of 4H-SiC UV SPADs.