  The most fundamental response of an ionized gas to a macroscopic object is
the formation of the plasma sheath. It is an electron depleted space charge
region, adjacent to the object, which screens the object's negative charge
arising from the accumulation of electrons from the plasma. The plasma sheath
is thus the positively charged part of an electric double layer whose
negatively charged part is inside the wall. In the course of the Transregional
Collaborative Research Center SFB/TRR24 we investigated, from a microscopic
point of view, the elementary charge transfer processes responsible for the
electric double layer at a floating plasma-wall interface and made first steps
towards a description of the negative part of the layer inside the wall. Below
we review our work in a colloquial manner, describe possible extensions, and
identify key issues which need to be resolved to make further progress in the
understanding of the electron kinetics across plasma-wall interfaces.
