  We present the results of a set of high resolution chemo-dynamical
simulations of dwarf galaxies in a $\Lambda$CDM cosmology. Out of an original
3.4 Mpc$^3$/h$^3$ cosmological box, a sample of 27 systems are zoomed-in from
z=70 to z=0. Gas and stellar properties are confronted to the observations in
the greatest details: in addition to the galaxy global properties, we
investigate the model galaxy velocity dispersion profiles, half-light radii,
star formation histories, metallicity distributions, and [Mg/Fe] abundance
ratios. The formation and sustainability of the metallicity gradients and
kinetically distinct stellar populations are also tackled. We show how the
properties of six Local Group dwarf galaxies, NGC 6622, Andromeda II, Sculptor,
Sextans, Ursa Minor and Draco are reproduced, and how they pertain to three
main galaxy build-up modes. Our results indicate that the interaction with a
massive central galaxy could be needed for a handful of Local Group dwarf
spheroidal galaxies only, the vast majority of the systems and their variety of
star formation histories arising naturally from a $\Lambda$CDM framework. We
find that models fitting well the local Group dwarf galaxies are embedded in
dark haloes of mass between $5\times 10^8$ to a few $10^9\,\rm{M_\odot}$,
without any missing satellite problem. We confirm the failure of the abundance
matching approach at the mass scale of dwarf galaxies. Some of the observed
faint however gas-rich galaxies with residual star formation, such as Leo T and
Leo P, remain challenging. They point out the need of a better understanding of
the UV-background heating.
