Charmonium is a bound state of a charmed quark and a charmed antiquark,and a charmoniumlike state is a resonant structure that contains a charmed quark and antiquark pair but has properties that are incompatible with a conventional charmonium state.While operating at center-of-mass energies from 2 to 5 GeV,the BESⅢ experiment can access a wide mass range ofcharmonium and charmoniumlike states,and has contributed significantly in this field.We review BESⅢ results involving conventional charmonium states,including the first observation of the M1 transition ψr (2S) → γ ηc(2S) and the discovery of the ψ2(3823) state;and report on studies ofcharmoniumlike states,including the discoveries of the Zc(3900)and Zc(4020) tetraquark candidates,the resolution of the fine structure of the Y(4260) state,the discovery of the new production process e+e-→ γX(3872) and the uncovering of strong evidence for the commonality among the X(3872),Y(4260) and Zc(3900) states.The prospects for further research at BESⅢ and proposed future facilities are also presented.