Abstract: The migration of bubbles ordroplets in liquids is a very important topic in materials science,chemical engineering and fundamental researches. Under themicro-gravity condition, if the temperature gradient of thebackground flow field is non-zero, bubbles or droplets will movebecause of differences in interfacial tension on the drop surface. Suchmotion is termed Marangoni migration or thermocapillary migration.In this paper, the progresses of researches on the drop/bubblethermocapillary migration, including theoretical analysis, numericalsimulation and experimental studies, are reviewed. At present, thetheoretical analyses mainly focus on linear or weaknon-linear steady problems. Some numerical simulations were carried outon unsteady migration processes of drops with the Marangoninumber less than 100. When the heat convection effect isstrong(over 100), no numerical results were reported that are consistent with those from experiments. In this paper, we summarizeprevious research results, give our new numerical resultsof unsteady drop migration problems with large Marangoni numbers anddiscuss new phenomena under this condition. Finally, some problems in current studies are pointed out and the developmentof drop thermocapillary migration problems in future is discussed.