Single domain walls can be multi-ferroic, (super-) conducting or good ionic conductors. Their intrinsic properties will be discussed. Their movement under external fields contains ballistic movements and jerks (flickering noise). Jerks provide the main structural singularities which can be measured by acoustic emission, and mechanical and electrical responses over large frequency ranges. The underlying physical properties of the wall movements are simulated by large-scale computer MD modelling and compared with simple models. .