Grain weight, as one of the three components, directly associates to the wheat yield production. Grain weight is recognized as a complex quantitative trait which is largely controlled by multiple functional genes/loci and which is also affected by genotype-environment interaction. The genes controlling the grain weight and its components are found to be distributed on each chromosome of three wheat sub-genomes. Many molecular markers in wheat grain weight assisted selection have become applicable.The advances on the genetic characteristics, gene location, molecular mechanism and external factors affecting the grain weight formation have made with the contributions of national and international scholars. In this paper, the composing factors and influencing factors of wheat grain weight have been reviewed. The genetic localization, molecular cloning and allelic variation mining of the underlying genes are described, and the development of gene-based functional markers as well as the application in marker assisted breeding are summarized, as well as the future research prospects of wheat grain weight are proposed.