Charged domain walls (CDWs) in ferroelectric materials raise both fundamental and practical interest due to their electrophysical properties differing from bulk ones. On a microstructure level, CDWs in ferroelectrics are 2D defects separating regions with different spontaneous polarization vector directions. Screening of electric field of the CDW's bound ionic charges by mobile carriers leads to the formation of elongated narrow channels with an elevated conductivity in initially dielectric materials. Controlling the position and inclination angle of CDW relative to the spontaneous polarization direction, one can change its conductivity over a wide range thus providing good opportunities for developing memory devices, including neuromorphic systems. This review describes the state of art in the formation and application of CDWs in single crystal uniaxial ferroelectric lithium niobate (LiNbO3, LN), as resistive and memristive switching devices. The main CDWs formation methods in single crystal and thin-film LN have been described, and modern data have been presented on the electrophysical properties and electrical conductivity control methods of CDWs. Prospects of CDWs application in resistive and memristive switching memory devices have been discussed.