Despite its success in explaining the large scale structure of the Universe, the standard model of cosmology (LCDM) has faced a number of problems in explaining the properties of dwarf galaxies. Detailed studies of these intrinsically faint objects are only possible in the Local Universe. The Local Group of galaxies therefore serves as a laboratory for studying galaxy formation scenarios and for testing predictions of cosmological models. I will introduce the APOSTLE project, a suite of high resolution hydrodynamical simulations of Local Group-like regions within the LCDM framework, and explain how the small scale problems of LCDM are resolved or persist in this model. I will particularly focus on the too-big-to-fail problem for MW satellites and its solution within LCDM and without requiring dwarf galaxies to have "cores" in their dark matter density profiles. I will extend the discussion to Andromeda satellites. Is there any too-big-to-fail problem in this system?
