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Halide perovskite semiconductors and solar cells respond to electric fields in a way that varies across time and length scales. We discuss the microscopic processes that give rise to the macroscopic polarization of these materials, ranging from the optical and vibrational response to the transport of ions and electrons. The strong frequency dependence of the dielectric permittivity can be understood by separating the static dielectric constant into its constituents, including the orientational polarization due to rotating dipoles, which connects theory with experimental observations. The controversial issue of ferroelectricity is addressed, where we highlight recent progress in materials and domain characterization but emphasize the challenge associated with isolating spontaneous lattice polarization from other processes such as charged defect formation and transport. We conclude that CH3NH3PbI3 exhibits many …