The Hinode satellite opens a new era to the sunspots research, because of its high spatial resolution and temporal stability. Fine scale structures in sunspots, called umbral dots (UDs), have become one of the hottest topics in terms of the close observation of the magnetoconvection. In this paper, a brief review of observed properties of UDs is given based on the recent literature. UDs born in the periphery of the umbra exhibit inward migration, and their speeds are positively correlated with

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... he magnetic field inclination. Longer-lasting UDs are tend to be larger and brighter, while lifetimes of UDs show no relation with their background magnetic field strength. UDs tend to disappear or stop its proper motion by colliding with the locally strong field region. The spatial distribution of UD is not uniform over an umbra but is preferably located at boundaries of cellular patterns. From our 2-dimensional correlation analysis, we measured the characteristic width of the cell boundaries (~0.5") and the size of the cells (~6"). Then we performed a simplified analysis to get statistics how the UD distribution is random or clustered using the Hinode blue continuum images. We find a hint that the UDs become less dense and more clustered for later phase sunspots. These results may be related to the evolutional change of the subsurface structure of a sunspot. Based on these observational results, we will discuss their physical models by means of numerical simulations of magnetoconvection.