Understanding the combustion process is essential for the energy utilization in a safe, efficient and clean way. However, in normal gravity, the buoyant convection and gravitational sedimentation make the process complicated. Such effects nearly disappear in microgravity, which will simplify the research on combustion. In view of the combustion process occured on ground and the fire safety problem for manned spacecraft, the research on microgravity combustion involves various fields of combustion science, including premixed gas combustion, gaseous diffusion combustion, droplet combustion, particle combustion, dust combustion and flame spread over fuel surface, during the development of about a half century, especially the last decade. Through the research, the droplet combustion with spherical symmetry, dust combustionwithout sedimentation effect and combustion in quiescent or low speed convection environment have been realized, the flame ball, self-extinguishing flame and other phenomena were observed, and the thermophoresis effect during soot formation, flammability limit and flame instability and other mechanism were clarified. The research has deepened the knowledge of combustion phenomenon and especially deepened the understanding on radiation effect. It is shown that, for premixed gas combustion, gaseous diffusion combustion and droplet combustion, there is also the quenching extinction limit caused by large radiative heat loss, besides the blowoff extinction limit caused by short residence time. The former can be found only under microgravity condition. Some of these results have already been absorbed into the textbook. The fact that the combustion under microgravity shows different characteristics from that under normal gravity is important for fire safety for manned spacecraft. Acounting for the condition of our country and present research advances, the coal particle combustion, the dust combustion, the mechanism related to soot, radiation effect andchemical dynamics would serve as the promising future directions.