**Abstract**

Macroscopic nonlinearity and hysteresis observed in the piezoelectric and dielectric responses of ferroelectric materials to external stimuli are commonly attributed to localized displacements of domain walls (DWs). The link between the macroscopic response and microscopic DW dynamics is provided by the well-known Rayleigh relations, extensively used to quantify the electrical and electromechanical behavior of ferroelectric ceramics and thin films under subswitching conditions. In this chapter, I will present an intriguing case where DWs exhibit enhanced electrical conductivity with respect to the bulk conductivity. By combining experimental data and modeling, it will be shown that the local conductivity, related to accumulation of charged points defect at DWs, does not only affect DW dynamics through DW-defect pinning interactions, as we may expect, but goes beyond it by affecting the macroscopic nonlinearity and hysteresis in a more complex manner. The major characteristics and implications of the underlying nonlinear Maxwell-Wagner piezoelectric relaxation, triggered by the presence and dynamics of conducting DWs, will be presented, reviewed and discussed in the framework of systematic multiscale analyses on BiFeO3 ceramics. The result may have implications in the development of promising BiFeO3 based compositions for high-temperature piezoelectric applications.

**Keywords:** Piezoelectric, nonlinearity, hysteresis, domain wall, electrical conductivity, BiFeO3
