  The evidence for the key role of the $\sigma$ bands in the electronic
properties of MgB$_2$ points to the possibility of nonadiabatic effects in the
superconductivity of these materials. These are governed by the small value of
the Fermi energy due to the vicinity of the hole doping level to the top of the
$\sigma$ bands. We show that the nonadiabatic theory leads to a coherent
interpretation of $T_c = 39$ K and the boron isotope coefficient $\alpha_{\rm
B} = 0.30$ without invoking very large couplings and it naturally explains the
role of the disorder on $T_c$. It also leads to various specific predictions
for the properties of MgB$_2$ and for the material optimization of these type
of compounds.
