  Many of the $XYZ$ resonances observed by the Belle, Babar, CLEO and BESIII
collaborations in the past decade are difficult to interpret as conventional
quark-antiquark mesons, motivating the consideration of scenarios such as
multi-quark states, meson molecules, and hybrids. After a brief introduction to
QCD sum-rule methods, we provide a brief but comprehensive review of the mass
spectra of the quarkonium-like tetraquark states $qQ\bar q\bar Q$, doubly
charmed/bottomed tetraquark states $QQ\bar q\bar q$ and the heavy quarkonium
hybrid states $\bar QGQ$ in the QCD sum rules approach. Possible
interpretations of the $XYZ$ resonances are briefly discussed.
