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The past decade witnessed a remarkable proliferation of exotic charmonium-like resonances discovered at accelerators. In particular, the recently observed charged states are clearly not interpretable as qq mesons. Notwithstanding the considerable advances on the experimental side, conflicting theoretical descriptions do not seem to provide a definitive picture about the nature of the so called XY Z particles. We present here a comprehensive review about this intriguing topic, discussing both those experimental and theoretical aspects which we consider relevant to make further progress in the field. At this state of progress, XY Z phenomenology speaks in favour of the existence of compact four-quark particles (tetraquarks) and we believe that realizing this instructs us in the quest for a firm theoretical framework.

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The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. In this study we start from the 3 → 3 scattering amplitude for spinless particles, which contains an isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the latter, we derive a relativistic three-dimensional scattering equation that manifestly fulfills three-body unitarity and two-body unitarity for the sub-amplitudes. This property holds for energies above breakup and also in the presence of resonances in the sub-amplitudes.