  Since 2003 many charmonium-like states were observed experimentally.
Especially those charged charmonium-like $Z_c$ states and bottomonium-like
$Z_b$ states cannot be accommodated within the naive quark model, which are
good candidates of either the hidden-charm tetraquark states or molecules
composed of a pair of charmed mesons. In 2015, the LHCb Collaboration
discovered two hidden-charm pentaquark states, which are also beyond the quark
model. In this talk, 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.
