Abstract
We present recent results on the effort to simulate the Local Group (LG, composed by the Milky Way and M31) in an explicit cosmological context. The main results are obtained using cosmological N-body simulations that use constrained initial conditions aiming at reproducing the observed large scale environment. We find that in these simulations there is a bias in the formation properties of the LG with respect to a random sample. We also show that the observed radial motion of Andromeda towards us is not common in the context provided by ΛCDM.