Refined calculations of transport phenomena are likely to be in demand in the emerging era of multi-messenger neutron star observations. The outer core of neutron stars presumably consists of a dense plasma comprised of degenerate electrons, muons, protons, and neutrons. Transport phenomena in this region are of particular phenomenological relevance as they impact the damping of hydrodynamic modes and r-modes, the thermal relaxation, and the spin evolution of neutron stars. In this talk, the microscopic physics that determine transport such as screening and damping effects are briefly reviewed. A particular focus is placed on the impact of electron-neutron scattering induced by medium effects.