  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 4.9 GeV,
the BESIII experiment can access a wide mass range of charmonium and
charmoniumlike states, and has contributed significantly in this field. We
review BESIII results involving conventional charmonium states, including the
first observation of M1 transition $\psi(3686) \to \gamma \eta_c(2S)$ and the
discovery of the $\psi_2(3823)$; and report on studies of charmoniumlike
states, including the discoveries of the $Z_c(3900)$ and $Z_c(4020)$ tetraquark
candidates, the resolution of the fine structure of the $Y(4260)$, the
discovery of the new production process $e^+e^-\to \gamma X(3872)$, and the
uncovering of strong evidence for the commonality among the $X(3872)$,
$Y(4260)$, and $Z_c(3900)$ states. The prospects for further research at BESIII
and proposed future facilities are also presented.
