The Local Group offers an excellent laboratory for near-field cosmology by permitting us to use the resolved stellar content of its constituent galaxies as probes of galaxy formation and evolution, which in turn is an important means for testing cosmological models of hierarchical structure formation. In this review, we discuss the the least massive, yet most numerous type of galaxy in the Local Group, the dwarf spheroidal galaxies, and compare their properties to cosmological predictions. In particular, we point out problems found with a simple building block scenario and with effects expected from reionization. We show that the star formation histories of dSphs are inconsistent with the predicted cessation of star formation after reionization; instead, extended star formation episodes are observed. The Galactic dSphs contain in part prominent intermediate-age populations, whereas the Galactic halo does not. Conversely, the M31 dSphs are almost entirely old, while the M31 halo contains a substantial intermediate-age population. These differences in the population structure as well as the differences in the modes of star formation inferred from [α/Fe] ratios make dSphs unlikely major contributors to the build-up of the Galactic and M31 halo unless most of the accretion occurred at early epochs. On the other hand, there is clear evidence for ongoing harassment and accretion of a number of dSphs.