  We present extensive Scanning Tunneling Spectroscopy (STM/S) measurements at
low temperatures in the multiband superconductor MgB$_2$. We find a similar
behavior in single crystalline samples and in single grains, which clearly
shows the partial superconducting density of states of both the $\pi$ and
$\sigma$ bands of this material. The superconducting gaps corresponding to both
bands are not single valued. Instead, we find a distribution of superconducting
gaps centered around 1.9mV and 7.5mV, corresponding respectively to each set of
bands. Interband scattering effects, leading to a single gap structure at 4mV
and a smaller critical temperature can be observed in some locations on the
surface. S-S junctions formed by pieces of MgB$_2$ attached to the tip clearly
show the subharmonic gap structure associated with this type of junctions. We
discuss future developments and possible new effects associated with the
multiband nature of superconductivity in this compound.
