Due to the recent experimental breakthrough in heavy ion collisions about the spin polarization measurements, the QCD matter under rotation attracts a lot of attentions. Many novel phenomena are under intensive discussions, like the hyperon spin polarization, vector meson spin alignment, chiral vortical effects, and so on. It would be also interesting to ask what would be the effect of a global rotation on the QCD phase structure. The natural expectation would be that due to the spin polarization by rotation, all the spin-0 condensate, like the chiral condensate, would be unfavored and thus the chiral phase structure may vary under rotation. We will discuss whether this is the case for QCD by either model discussion and by lattice simulation. We will also discuss the confinement-deconfinement transtion under rotation.