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Ferroelectrics such as LiNbO_{3} (LN) are wide-band-gap insulators that may show a high local electric conductivity at the domain walls (DWs). The latter are interfaces separating regions of noncollinear polarization, which can be manipulated to build integrated nanoelectronic elements. In the present work, we model different DW types in LN from first principles. Our models reveal the DW morphology and shed light on their electronic properties: A strong band bending is predicted for charged DWs, leading to local metallicity. Defect trapping at the DW may further enhance the electric conductivity.