The migration phenomena of bubbles or droplets in liquids are very interesting topics in material science, chemical engineering, and fundamental research. Under the zerogravity condition, if the temperature gradient of the background fluid is nonzero, bubbles or droplets will move because the variance of interfacial tension on the drop can produce a shear stress on both sides of the interface. As a result, the bubbles/drops will move from the cold side to the warm side of the background fluid. Such motion is termed thermocapillary migration. Recently, some research progress has been made by a team in National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences. Researchers solved the axisymmetric Navier–Stokes equations coupled with the energy equation by the finite-difference front-tracking scheme. They gave out detailed discussions and physical explanations on this phenomenon for different values of Marangoni numbers, Reynolds numbers etc. It is found that Marangoni number have a significant influence on drop migration velocity. When Marangoni number is large, heat convection will lead to redistributions of temperature fields inside the drops and cause the overshoot phenomena. Reynolds numbers have only slight impact on the migration velocity but can affect the accelerating process obviously. The ratio of drop viscosity to mother liquid has the most important effect on migration velocity, and the enlargement of the drop speed caused by bigger viscosity ratio is higher than linear growth. The overshoot phenomena of migration velocities have been reported before. In the case of bubble migration, the deformation is important. However, the researchers found that overshoot phenomena of drop velocities are mainly caused by the redistributions of temperature fields inside drops. The viscosity force of the background liquid can be viewed as the driving force and the resistance of the drop migration simultaneously. Based on this understanding, researchers explained why bigger Reynolds numbers result in lower final migration speeds. The main results of this research were published in the article section of the journal Phy. Fluids, with 20 pages, 35 figures and two movies: Zhaohua Yin, Peng Gao, Wenrui Hu & Lei Chang, 20, 082101(2008), http://dx.doi.org/10.1063/1.2965549.