  In the past decade many charmonium-like states were observed experimentally.
Especially those charged charmonium-like $Z_c$ 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.
