This paper is devoted to the study of QCD properties affected by relativistic rotation. The presented results were obtained within the first-principle lattice simulation of gluodynamics and in QCD with dynamical quarks. We discuss how relativistic rotation influences confinement/deconfinement and chiral symmetry breaking/restoration phase transitions. We also focus on the moment of inertia of gluon plasma, which unexpectedly takes a negative value below the ‘‘supervortical temperature’’ $T_{s}=1.50(10)T_{c}$, vanishes at $T=T_{s}$, and becomes a positive quantity at higher temperatures. The negative moment of inertia indicates a thermodynamic instability of rigid rotation. Finally, we discuss the spatial structure of rotating gluon plasma and demonstrate the emergence of an inhomogeneous phase transition in a certain range of temperatures and rotation velocities.