Abstract: In the past 12 years, dozens of charmonium-like states have been reported in experiment. Facing so abundant novel phenomena, theorists have been hard at work to reveal the underlying mechanism relevant to these XYZ states. A concise review of the observed XYZ states is first given. Then, an introduction is presented to the theoretical progress made by our group in the study of XYZ states, which includes ① the hadronic molecular state explanations to Y(3940), Y(4140) and Y(4274); ② the non-resonant explanation to Y(4260) and Y(4360); ③ the P-wave charmonium assignment to Y(3915), Z(3930) and X(4350); ④ the initial single pion emission mechanism and the observation of Zc(3900).

Key words: charmonium-like states, non-perturbative QCD, phenomenological model