Simulations of the early structure formation and the Epoch of Reionization have now reached sufficient volume, dynamic range and resolution to make reliable predictions for the fundamental features and observable signatures of these epochs. I will review recent progress we have made in this area, which include performing the largest and most detailed early structure formation and EoR simulations. I will discuss the various observational signatures we predict, with a particular focus on the best observational strategies. I will also present some of our recent results on the reionization history of the Local Group of galaxies using constrained simulations of its formation.