Dark matter makes up most of the mass of the Universe but remains
mysterious. I discuss recent progress in constraining its properties by
measuring its distribution inside tiny dwarf galaxies. I present the first
observational evidence that dark matter at the centres of dwarfs is pushed
outwards by baryonic feedback during galaxy formation. I show that this effect
can occur even in the very smallest "ultra-faint" dwarfs, and I present
observational evidence for this having happened in Eridanus II. I go on to
show how the densest dwarfs provide competitive constraints on
"self-interacting" and "wave"-like dark matter, and I show how future surveys
will place unprecedented constraints on the mass of a thermal relic dark
matter particle.