  We review our theoretical analysis of repulsively interacting three-component
fermionic atoms in optical lattices. We discuss quantum phase transitions at
around half filling with a balanced population by focusing on Mott transitions,
staggered ordering, and superfluidity. At half filling (with 3/2 atoms per
site), characteristic Mott transitions are induced by the anisotropic
interactions, where two-particle repulsions between any two of the three colors
have different strengths. At half filling, two types of staggered ordered
states appear at low temperatures depending on the anisotropy of the
interactions. As the temperature increases, phase transitions occur from the
staggered ordered states to the unordered Mott states. Deviating from half
filling, an exotic superfluid state appears close to a regime in which the Mott
transition occurs. We explain the origin of these phase transitions and present
the finite-temperature phase diagrams.
