Marangoni flow, which is driven by unbalanced surface tension caused by tem
perature or concentration gradient, plays an important role in mass and hea
t transport in crystal growth of floating zone. Half-zone model, which is s
implified from floating zone model, is one of typical models to the study o
f Marangoni convection. Recent numerical and experimental studies on Marang
oni convection in half-zone are reviewed, The importance of direct numerica
l simulation is stressed.