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We report on theoretical and experimental study of the spin polarization recovery and Hanle effect for the charge carriers interacting with the fluctuating nuclear spins in the semiconductor structures. We start the theoretical description from the simplest model of static and isotropic nuclear spin fluctuations. Then we describe the modification of the polarization recovery and Hanle curves due to the anisotropy of the hyperfine interaction, finite nuclear spin correlation time, and the strong pulsed spin excitation. For the latter case, we describe the resonance spin amplification effect in the Faraday geometry and discuss the manifestations of the quantum Zeno effect. The set of the experimental results for various structures and experimental conditions is chosen to highlight the specific effects predicted theoretically. We show that the spin polarization recovery is a very valuable tool for addressing carrier spin dynamics in semiconductors and their nanostructures.