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Ferroelectric domain walls are quasi‐2D systems that show great promise for the development of nonvolatile memory, memristor technology, and electronic components with ultrasmall feature size. Electric fields, for example, can change the domain wall orientation relative to the spontaneous polarization and switch between resistive and conductive states, controlling the electrical current. Being embedded in a 3D material, however, the domain walls are not perfectly flat and can form networks, which leads to complex physical structures. In this work, the importance of the nanoscale structure for the emergent transport properties is demonstrated, studying electronic conduction in the 3D network of neutral and charged domain walls in ErMnO₃. By combining tomographic microscopy techniques and finite element modeling, the contribution of domain walls within the bulk is clarified and the significance of curvature effects for the local conduction is shown down to the nanoscale. The findings provide insights into the propagation of electrical currents in domain wall networks, reveal additional degrees of freedom for their control, and provide quantitative guidelines for the design of domain‐wall‐based technology.