  In the quark model, hadrons are dominantly bound states of quark-antiquark
pairs (mesons) or three quarks (baryons), but QCD also allows hadronic states
to be composed of more quarks bound together. Recently, BESIII, Belle and LHCb
have confirmed the existence of four-quark and pentaquark candidates. These new
states, along with experimentally observed resonances that do not fit well into
the charmonium and bottomonium spectra, present challenges and opportunities
for strong interaction theory. In this talk, I will review results on
charmonium-like exotic quark states that have been observed by the BESIII
experiment at the Beijing Electron Positron Collider II (BEPCII).
