  The theoretical explanations about the ``Rho-pi puzzle'' in charmonium decays
are reviewed extensively, and the comparison of theoretical predications with
experimental data is made whenever possible. Three methods to estimate the
ratio of the branching fractions of J/psi and psi' decays are also discussed.
It is pointed out that in order to understand the Rho-pi puzzle, and the
dynamics of charmonium decays, systematic studies should be made in theory,
phenomenology and experiment aspects.
