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.
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