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Milky Way (MW) satellites reside within dark matter (DM) subhalos with abroad distribution of circular velocity profiles. This diversity is enhancedwith the inclusion of ultra-faint satellites, which seemingly have very high DMdensities, albeit with large systematic uncertainties. We argue that ifconfirmed, this large diversity in the MW satellite population poses a serioustest for the structure formation theory with possible implications for the DMnature. For the Cold Dark Matter model, the diversity might be a signature ofthe combined effects of subhalo tidal disruption by the MW disk and strongsupernova 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$^{-1}$ wheresubhalos have too low densities to explain the ultra-faint galaxies. We proposea novel solution to explain the diversity of MW satellites based on thegravothermal collapse of SIDM haloes. This solution requires avelocity-dependent cross section that predicts a bimodal distribution of cuspydense (collapsed) subhaloes consistent with the ultra-faint satellites, andcored lower density subhaloes consistent with the brighter satellites.

The diverse dark matter density at sub-kiloparsec scales in Milky Way satellites:implications for the nature of dark matter