Ferroelectric domain walls (DWs), i. e. the narrow transition zones between\nindividual ferroelectric domains (regions of constant spontaneous dielectric polarization),\nhave attracted a continuously rising research interest throughout\nthe past decade. This is due to the fact that DWs exhibit minute thicknesses\non the unit cell level only, thus constituting embedded two-dimensional\nnanosheets with distinct electronic and chemical properties that may drastically\ndier from the surrounding bulk. Moreover, they can be positioned and\nrecongured practically at will, for instance by applying external elds.\nThis cumulative habilitation thesis specically addresses the pronounced\nelectrical conductivity of DWs in otherwise almost perfectly insulating lithium\nniobate (LiNbO3) single crystals, that has been extensively studied at the\nInstitute of Applied Physics, TU Dresden, Germany. Thereby we were able to\nestablish a clear connection between conductivity and geometry of such DWs.\nFurthermore, we have developed protocols to deliberately enhance the current\nthrough a single DW by several orders of magnitude, applying a subsequent\ntuning treatment to as-poled domains. Characterization techniques used in\nthese experiments include DC and AC conductive atomic force microscopy,\nmacroscopic transport measurements, photoelectron emission microscopy, as\nwell as three-dimensional DW imaging by second harmonic microscopy and\noptical coherence tomography, and the modeling of conductive paths along\nthe DWs using resistor networks.