  We review recent developments in lattice siumulations of the equation of
state, order of the thermal phase transition and the determination of the
pseudo-critical temperature in (2+1)-flavor QCD. Owing to the increasing
computer power, new argothithms, and improved fermion formulations, studies of
bulk QCD matter are approaching to the stage of precision science. We also
review recent lattice studies on the spectral properties of heavy quarkoniums
inside the quark-gluon plasma (QGP). Although they are still in an exploratory
stage, interesting physics in relation to the strongly correlated QGP is being
extracted.
