Transport dynamics of magma is an important branch of dynamics of magma, and its research contents contain five parts, including transport pattern, path, channel, driving force and mineralization during transport processes. Advances of all the five contents are systemically reviewed, and some potential important scientific questions are summarized, such as transport pattern of magma in the upper mantle, driving force for magma to ascent and formation mechanism of melt created fractures in elastic lithosphere, re-transport mechanism of magmas stagnated in chamber, and enrichment of elements and mineralization related to crystallization and differentiation of magma and interaction between magma and wall rocks during stagnation and transport processes of magma, in this contribution.