jats:pIn this Perspective, two interrelated new developments are discussed. The first relates to a much better understanding of the actual movement of domain walls during switching. Ferroelectric and ferroelastic domain movements proceed via the combination of jerky and smooth displacements of domain walls. A careful separation of these two mechanisms into “wild” and “mild” is crucial for the understanding of avalanches in ferroelectrics. Avalanche switching involves jerky domain wall movements and leads to singularities in the switching current. During avalanches, domain walls enhance and localize atomic transport and generate magnetism emerging from mobile kinks in the walls. The second development is based on the transport of dopants inside domain walls during nano-fabrication of devices. Progressing domain walls in electric fields can then—mainly in the case of wild wall movements—connect defect “reservoirs” similar to synapses connecting neurons in the brain. The walls take the role of synapses, and the defect clusters take that of neurons. The combination of fast moving domain walls and chemical transport inside the walls constitutes, therefore, ingredients for memristive device elements in neuromorphic computers. This application is predicted to play a major future role in ferroelectricity.</jats:p>