abstract: I will survey old and new results on the Boltzmann-Grad limit of the Lorentz gas. I will in particular focus on recent results with Andreas Strombergsson (Uppsala) for the case of quasicrystalline scatterer configurations, and also discuss the Boltzmann-Grad limit for quantum transport in the case of smooth periodic potentials, which is joint work with Jory Griffin (Queens University, Canada).