Charged domain walls (CDWs) in proper ferroelectrics are a novel route towards the creation\nof advancing functional electronics. At CDWs the spontaneous polarization obeying\nthe ferroelectric order alters abruptly within inter-atomic distances. Upon screening, the\nresulting charge accumulation may result in the manifestation of novel fascinating electrical\nproperties. Here, we will focus on electrical conduction. A major advantage of these\nferroelectric DWs is the ability to control its motion upon electrical fields. Hence, electrical\nconduction can be manipulated, which can enrich the possibilities of current electronic\ndevices e.g. in the field of reconfigurability, fast random access memories or any kind of\nadaptive electronic circuitry.\nIn this dissertation thesis, I want to shed more light onto this new type of interfacial\nelectronic conduction on inclined DWs mainly in lithium niobate/LiNbO3 (LNO). The\nexpectation was: the stronger the DW inclination towards the polar axis of the ferroelectric\norder and, hence, the larger the bound polarization charge, the larger the conductivity to\nbe displayed.\nThe DW conductance and the correlation with polarization charge was investigated\nwith a multitude of experimental methods as scanning probe microscopy, linear and nonlinear\noptical microscopy as well as electron microscopy. We were able to observe a clear\ncorrelation of the local DW inclination angle with the DW conductivity by comparing the\nthree-dimensional DW data and the local DW conductance.\nWe investigated the conduction mechanisms on CDWs by temperature-dependent twoterminal\ncurrent-voltage sweeps and were able to deduce the transport to be given by\nsmall electron polaron hopping, which are formed after injection into the CDWs. The\nthermal activated transport is in very good agreement with time-resolved polaron luminescence\nspectroscopy. The applicability of this effect for non-volatile memories was\ninvestigated in metal-ferroelectric-metal stacks with CMOS compatible single-crystalline\nfilms. These films showed unprecedented endurance, retention, precise set voltage, and\nsmall leakage currents as expected for single crystalline material. The conductance was\ntuned and switched according to DW switching time and voltage. The formation of CDWs\nhas proven to be extremely stable over at least two months. The conductivity was further\ninvestigated via microwave impedance microscopy, which revealed a DW conductivity of\nabout 100 to 1000 S/m at microwave frequencies of about 1 GHz.