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We present recent advances in the generation of highly intense multiterahertz transients and their application to nonlinear spectroscopy of bulk semiconductors. An optimized scheme of parametric amplification results in broadband single- or few-cycle terahertz transients with peak electric fields up to 10 or 25 MV/cm, respectively. Time-resolved four-wave mixing terahertz spectroscopy of InSb far away from the interband resonance demonstrates clear signatures of a nonperturbative regime of Rabi flopping. We qualitatively explain the observed behavior within a model of a quantum two-level system. In addition, we demonstrate the dynamical Franz-Keldysh effect in InP resolved on a subcycle timescale. The field-induced modulation of the interband optical absorption at the second harmonic of the driving terahertz field is observed in full agreement with theoretical predictions.