Topological walls separating domains of continuous polarization, magnetization, and strain in ferroic materials hold promise of novel electronic properties, that are intrinsically localized on the nanoscale and that can be patterned on demand without change of material volume or elemental composition. We have revealed that ferroelectric domain walls in multiferroic BiFeO(3) are inherently dynamic electronic conductors, closely mimicking memristive behavior and contrary to the usual assumption of rigid conductivity. Applied electric field can cause a localized transition between insulating and conducting domain walls, tune domain wall conductance by over an order of magnitude, and create a quasicontinuous spectrum of metastable conductance states. Our measurements identified that subtle and microscopically reversible distortion of the polarization structure at the domain wall is at the origin of the dynamic conductivity. The latter is therefore likely to be a universal property of topological defects in ferroelectric semiconductors.