The nature of Dark Matter (DM) is a key question in modern Physics and Cosmology. To date the problem remains wide open, to the point that it is not yet known whether DM is made of exotic particles which formed shortly after the Big Bang or a manifestation of gravitational interactions that go beyond General Relativity. In this talk I will argue that the non-linear growth of structures in the Universe holds detailed information on the microscopic properties of DM. In this context, dwarf spheroidal galaxies, being the faintest, smallest and most DM-dominated galaxies known to us, provide excellent laboratories to test a wide range of cosmological theories on galactic scales. Finally, I will review current constraints on a Warm, Self-Interacting and Axion DM model derived from the chemo-dynamical modelling of Milky Way dwarf spheroidals and discuss future opportunities in this field.