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 the 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 ( \approx 0.5 \arcsec ) and the size of the cells ( \approx 6 \arcsec ) .

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 .