This review presents briefly two aspects of Galactic interstellar medium science that seem relevant for studying EoR. First, we give some statistical properties of the Galactic foreground emission in the diffuse regions of the sky. The properties of the emission observed in projection on the plane of the sky are then related to how matter is organised along the line of sight. The diffuse atomic gas is multi-phase, with dense filamentary structures occupying only about 1% of the volume but contributing to about 50% of the emission. The second part of the review presents aspect of structure formation in the Galactic interstellar medium that could be relevant for the subgrid physics used to model the formation of the first stars.