\section{Heavy quarkonium spectroscopy}
The bound state of two heavy quarks has low enough energies that its 
spectroscopy is close to the non-relativistic interpretations of the 
atoms. The quantum numbers that are more appropriate to characterize a 
state are therefore, in decreasing order of energy splitting among 
different eigenstates, the radial excitation ($n$), the spatial angular 
momentum $L$, the spin $S$ and the total angular momentum $J$. Given 
this set of quantum numbers, the parity and charge conjugation of the 
states are derived by $P=(-1)^(L+1)$ and $C=(-1)^)L+S)$. 
Fig.~\ref{fig:quarkon} shows the mass and quantum number assignments of 
the 
well established charmonium and bottomonium states.
\begin{figure*}[!htb]
 \begin{tabular}{lr}
% \rotatebox{0}{
\epsfig{file=charmon_proceed.eps,height=6cm}%} 
&
% \rotatebox{0}{
\epsfig{file=bottom_proceed.eps,height=6cm}%}\\
\end{tabular}
 \caption{\it Charmonium (left) and Bottomonium (right) states with 
$L<=2$. The theory predictions are according to the potential models 
described in Ref.~\cite{Brambilla:2004wf}. 
 }
    \label{fig:quarkon}
\end{figure*}

\subsection{Charmonium spectroscopy}
Figure~\ref{fig:quarkon}a shows that all the predicted states below open charm
 threshold have been observed, leaving the search open only to states above the
 threshold. In this field the lastest developments concern the measurement of 
the paramaters and the quantum number assignment for the $J^{PC}=1^{--}$ 
states.

The BES collaboration has recently performed a fit to the $R$ scan 
results which takes into account interference between resonances more 
accurately~\cite{Ablikim:2007gd}. The updated parameters are reported in Tab.~\ref{tab:rscan}, compared with the most recent determinations.
 
\begin{table*}[!htb]
\begin{center} 
\caption{ 
Most recent determination of the  $J^{PC}=1^{--}$  charmonium states from BES~\cite{Ablikim:2007gd}, compared to the 2006 edition of the PDG~\cite{Yao:2006px} 
}
\label{tab:rscan} 

\begin{tabular}{|c|c|c|c|c|c|} \hline \hline
        &         &$\psi(3770)$  &$\psi(4040)$&$\psi(4160)$&$\psi(4415)$\\ \hline
$M$     &PDG2006  &3771.1$\pm$2.4&4039$\pm$1.0&4153$\pm$3  & 4421$\pm$4 \\
(MeV/$c^2$)          &BES '07 &3771.4$\pm$1.8& 4038.5$\pm$4.6 & 4191.6$\pm$6.0 & 4415.2$\pm$7.5\\\hline\hline
$\Gamma_{tot}$&PDG2006  &23.0$\pm$2.7&80$\pm$10    &103$\pm$8    &     62$\pm$20   \\
(MeV)         &BES '07      &25.4$\pm$6.5&81.2$\pm$14.4&72.7$\pm$15.1&73.3$\pm$21.2\\\hline\hline
\end{tabular} 
\end{center}
\end{table*}

The $J^{PC}=1^{--}$ assignment does not univocously identify the state, since both $^{2S+1}L_J=^3D_1$ and $^3D_1$ states would have it. The recent observation from Belle of the first exclusive decay of the $\psi(4415)\to DD^*_{2}(2460)$~\cite{belle:2007fq}, shows that this meson is predominantly $D$ wave. At the same time the study from CLEO-c of the $\psi(3770)\to\chi_{cJ}\gamma$~\cite{Briere:2006ff} confirms the dominance of the $D$ wave also in this meson. Both these assignments confirm the theoretical predictions as shown in Fig.~\ref{fig:quarkon}a.

\subsection{Bottomonium transitions}
Figure~\ref{fig:quarkon}b shows that the panorama in the bottomonium sector is
 much less complete, since there is a large number of states below the open bottom 
threshold which have not yet been observed. Moreover there is no recent announcement on the topic.

There are on the contrary plenty of results on the transitions between $J^{PC}=1^{--}$ states, i.e. between $Y(nS)$ 
and $Y(mS)$ states. These transitions are relevant because it is possible to predict both the 
di-pion invariant mass spectrum in the case of $Y(nS)\to Y(mS)\pi^+\pi^-$ decays, and the relative rate between these 
decays and the $Y(nS)\to Y(mS)\eta$ decays. These transitions allow therefore stringent tests of low energy QCD, in particular
of the predicitons of the Multipole Expansion~\cite{Kuang:2006me}. 

Recent measurements of the $Y(4S)\to Y(2S)\pi^+\pi^-$ decays from BaBar~\cite{Aubert:2006bm} showed a discrepancy with 
the above-mentioned predictions. Since such predictions mutuated the matrix elements from PCAC, CLEO-c recently published a 
comprehensive study of $Y(3S)\to Y(mS)\pi^+\pi^-$ decays under more general assumpions~\cite{cleo:2007sja}: a fit to the two distributions ($m=1,2$)
letting the matrix elements float shows a good agreement with the data, thus confirming the validity of the model. 
