  In the past decade, due to the experimental observation of many
charmonium-like states, there has been a revival of hadron spectroscopy. In
particular, the experimental observation of charged charmonium-like, $Z_c$
states, and bottomonium-like, $Z_b$ states, represents a challenge since they
can not be accommodated within the naive quark model. These charged states are
good candidates of either tetraquark or molecular states and their observation
motivated a vigorous theoretical activity. This is a rapidly evolving field
with enormous amount of new experimental information. In this work, we review
the current experimental progress and investigate various theoretical
interpretations of these candidates of the multiquark states. The present
review is written from the perspective of the QCD sum rules approach, where we
present the main steps of concrete calculations and compare the results with
other approaches and with experimental data.
