  In the past two decades, a plethora of hadronic states beyond the
conventional quark model of $q\bar{q}$ mesons and $qqq$ baryons have been
observed experimentally, which motivated extensive studies to understand their
nature and the non-perturbative strong interaction. Since most of these exotic
states are near the mass thresholds of a pair of conventional hadrons, the
prevailing picture is that they are primarily hadronic molecules. In principle,
one can verify the molecular nature of these states by thoroughly comparing
their masses, decay widths, and production rates in a particular picture with
experimental data. However, this is difficult or impossible. First, quantum
mechanics allows for the mixing of configurations allowed by symmetries and
quantum numbers. Second, data are relatively scarce because of their small
production rates and the many difficulties in the experimental measurements. As
a result, other alternatives need to be explored. This review summarizes three
such approaches that can help disentangle the nature of the many exotic hadrons
discovered. In the first approach, based on the molecular interpretations for
some exotic states, we study the likely existence of multiplets of hadronic
molecules related by various symmetries, such as isospin symmetry, SU(3)-flavor
symmetry, heavy quark spin/flavor symmetry, and heavy antiquark diquark
symmetry. In the second approach, starting from some hadronic molecular
candidates, one can derive the underlying hadron-hadron interactions. With
these interactions, one can study related three-body systems and check whether
three-body bound states/resonances exist. In the third approach, one can turn
to the femtoscopy technique to derive the hadron-hadron interactions, hence
inaccessible. This technique provided an unprecedented opportunity to
understand the interactions between unstable hadrons.
