Chemical mechanical polishing (CMP), now regarded as the only method to obtain whole-wafer planarization and super-smooth surface without sub-surface defects, is usually employed as the final processing method for silicon carbide (SiC) wafer, but the processing efficiency of conventional SiC-CMP is too low to fulfill the current requirement. Aiming at surface quality and material removal rate (MRR) of polished single crystal SiC wafer, the current state of SiC-CMP research is discussed and categorized by CMP using different slurries, e.g. conventional alkaline colloidal silica base slurry, mixed abrasives slurry and slurries with strong oxidizers, respectively. Then from the viewpoint of improving the mechanical role, as well as the chemical one of CMP, the existing efficiency-enhancement methods of SiC-CMP, including the catalyst assisted polishing, electrochemical-mechanical polishing (ECMP), fixed abrasive polishing, and photo-catalyst assisted polishing are extensively reviewed and discussed. Analyses and discussions are conducted from the reviewed researches of SiC-CMP and its related efficiency-enhancement methods, the difficulties and future direction for further improvement on polishing MRR of single crystal SiC are proposed.