Nowadays, sapphire substrates are widely employed for GaN light emitting diodes (LEDs) due to their comparatively low cost, large diameter, high quality, optical transparency, and high temperature stability etc. However, in spite of its commercial importance and extended history, the machining of sapphire remains a challenge. In the manufacture of sapphire, chemical mechanical polishing (CMP) has been widely used to obtain a mirror surface on the sapphire substrate and minimize the subsurface damages. In this paper, published literature in the past decade on CMP of sapphire substrates is summarized. Recent investigations into material removal mechanism of CMP of sapphire substrates are introduced and advances in experimental studies are reviewed in terms of abrasives, sapphire crystal orientations, pad materials, and other process parameters (such as polishing pressure, pad rotational speed, and temperature etc.). Possible topics for future research are also discussed.