  Milky Way (MW) satellites reside within dark matter (DM) subhalos with a
broad distribution of circular velocity profiles. This diversity is enhanced
with the inclusion of ultra-faint satellites, which seemingly have very high DM
densities, albeit with large systematic uncertainties. We argue that if
confirmed, this large diversity in the MW satellite population poses a serious
test for the structure formation theory with possible implications for the DM
nature. For the Cold Dark Matter model, the diversity might be a signature of
the combined effects of subhalo tidal disruption by the MW disk and strong
supernova feedback. For models with a dwarf-scale cutoff in the power spectrum,
the diversity is a consequence of the lower abundance of dwarf-scale halos.
This diversity is most challenging for Self-Interacting Dark Matter (SIDM)
models with cross sections $\sigma/m_\chi\gtrsim1~$cm$^2$g$^{-1}$ where
subhalos have too low densities to explain the ultra-faint galaxies. We propose
a novel solution to explain the diversity of MW satellites based on the
gravothermal collapse of SIDM haloes. This solution requires a
velocity-dependent cross section that predicts a bimodal distribution of cuspy
dense (collapsed) subhaloes consistent with the ultra-faint satellites, and
cored lower density subhaloes consistent with the brighter satellites.
