4H silicon carbide (4H-SiC) substrate wafers without surface/subsurface damages and low surface roughness are ideal substrates for the development of power electronics and radio frequency (RF) microwave devices, which hold great promise in applications of new energy, rail transportation, smart grid and 5G communication. The processing of 4H-SiC substrate wafers includes slicing, grinding, lapping, polishing and cleaning. However, the surface damages (SDs) and subsurface damages (SSDs) introduced during the processing of 4H-SiC substrates affects the properties of 4H-SiC substrates and epitaxial layers, and thus the performance and reliability of devices based on 4H-SiC. This paper focuses on the formation and removal mechanisms of SDs/SSDs during the processing of 4H-SiC substrate wafers. Based on the detection method of SDs/SSDs, the morphologies and characterization approaches of SDs/SSDs are reviewed. Finally, three commonly used technologies for the removal SDs/SSDs, along with their technical advantages, development challenges and trends, are briefly discussed.