In the past decade many charmonium-like states were observed experimentally. Especially those charged charmoniumlike Z c states and bottomonium-like Z b states can not be accommodated within the naive quark model. These charged Z c states are good candidates of either the hidden-charm tetraquark states or molecules composed of a pair of charmed mesons. Recently, the LHCb Collaboration discovered two hidden-charm pentaquark states, which are also beyond the quark model. In this work, we review the current experimental progress and investigate various theoretical interpretations of these candidates of the multiquark states. We list the puzzles and theoretical challenges of these models when confronted with the experimental data. We also discuss possible future measurements which may distinguish the theoretical schemes on the underlying structures of the hidden-charm multiquark states.

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Since the discovery of the first charmed meson in 1976, many open-charm and open-bottom hadrons were observed. In 2003 two narrow charm-strange states [Formula: see text] and D (2460) were discovered by the BaBar and CLEO Collaborations, respectively. After that, more excited heavy hadrons were reported. In this work, we review the experimental and theoretical progress in this field.

We investigate the newly observed X (4500) and X (4700) based on the diquark-antidiquark configuration within the framework of QCD sum rules. Both of them may be interpreted as the D-wave cscs tetraquark states of J P = 0 + , but with opposite color structures, which is remarkably similar to the result obtained in Chen and Zhu (Phys Rev D 83:034010, 2011) that X (4140) and X (4274) can be both interpreted as the S-wave cscs tetraquark states of J P = 1 + , also with opposite color structures. However, the extracted masses and these suggested assignments to these X states do depend on these running quark masses where m s (2 GeV) = 95 ± 5 MeV and m c (m c ) = 1.23 ± 0.09 GeV. As a byproduct, the masses of the hidden-bottom partner states of X (4500) and X (4700) are extracted to be both around 10.64 GeV, which can be searched for in the ϒφ invariant mass distribution.