Dwarf spheroidal (dSph) galaxies may represent a keystone to test predictions from the present cosmological paradigm : Cold Dark Matter (CDM). Firstly, dSphs are the most dark matter-dominated galaxies in the Universe known thus far and provide an ideal testbed to study the elusive nature of dark matter. Secondly, dSphs are also the faintest galaxies in the Universe and as such play a key role in galaxy formation models. In this talk I will discuss how Local Group dSphs can be used to put strong constraints on galaxy formation/evolution processes in the present cosmological paradigm. Our methods go from analytical models that assume dynamical equilibrium to high-resolution N-body simulations. I will show that our results provide a remedy for the « missing satellite problem » and prove the low efficiency of dark matter halos to form stars as the galaxy mass decreases. In addition, N-body experiments that simulate the evolution of dSphs in the host’s tidal field will be presented. Our results show that dSphs are extremely resilient to tidal mass stripping : a dSph must lose practically all the dark matter beyond the luminous radius (approx. 90—99% of the initial virial mass) before starting to shed its stars. Our simulations also show that tidal evolution occurs in a way that preserves the scaling relations observed in the Local Group dSph population. Finally, I will discuss what type of signatures are expected in dSphs that have lost a fraction of their stars to tides.