Understanding the phase structures of strong interaction matter is an active frontier in nuclear physics research currently, and it will provide crucial insights into heavy-ion collision experiments as well as neutron star observations. Most studies in this area focus on the influence of extremely high temperatures and baryon densities on matter properties, especially pertaining to phase transitions such as the chiral symmetry breaking and color superconductivity. Recent experimental and theoretical studies reported that in non-central heavy-ion collisions, systems carry a large initial angular momentum that becomes very strong vorticity fields in the bulk fluid. This has thus introduced several new questions regarding the properties of strong interaction matter under vorticity fields, and have led to many novel results. Thermal field theory calculations based on rotating frame and mean-field approximation have been developed to study various phase transitions under rotation, such as chiral symmetry breaking, color superconductivity and superfluidity at high isospin asymmetry. The results have demonstrated important impacts of vorticity fields on the phase boundaries of these transitions, and have also revealed nontrivial new phase structures of strong interaction matter under rotation. A new dimension of the usual QCD phase diagram has been unveiled. The study of rotation-induced phase transition extends phase transition research to a broader space. There remain more unexplored issues that merit further study.