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.