This book is proposed by a group of scientists and a space-agency engineer who performed collaboratively a series of microgravity experiments on the thermocapillary convection in a liquid bridge in microgravity aboard the International Space Station. This chapter discusses advancements in research on thermocapillary convection in finite-length liquid bridges, which was initially motivated by the growth of single crystals. The chapter begins by introducing explanatory research in this field, followed by the descriptions of the formation of hydrothermal waves, including the condition of their transition, their course of development in the flow field, with a particular focus on the effects of dimensions, heat exchange with the surroundings, and gravity. Several pioneering microgravity experiments using sounding rockets are described. Additionally, we will focus on the particle accumulation structure (PAS), mentioning its discovery, the various patterns of its appearance, and subsequent related studies through both experimental and numerical analyses. Finally, recently developed applications related to microfluidics will be briefly introduced.