Modern modulation methods as used in 3rd generation mobile communications (UMTS) generate strongly fluctuating transmission signal envelopes with high peak-to-average power ratios. These properties result in significant distortion due to the nonlinear behavior of the radio-frequency power amplifier (RF PA). We propose different nonlinear model structures for such amplifiers, based on memory polynomials and frequency-domain Volterra kernel expansion, where we can reduce the number of free parameters by 80 % compared to traditional Volterra series approaches. Because these nonlinear models incorporate memory, we are able to model the nonlinear distortion of RF PAs with sufficient accuracy (e.g., -30 dB relative modeling error ), including the wideband case (bandwidth B=20 MHz as needed for four-carrier WCDMA). Furthermore, we propose a method to construct RF PA models from frequency-dependent AM/AM and AM/PM conversions. For the compensation of the nonlinearities, we analyze and simulate different digital predistorter structures in terms of complexity and linearization performance. As a result, memory-polynomial predistorters (7th order) can achieve a linearization performance comparable to the full Volterra predistorter, while the number of parameters is reduced from 42 to 11. Finally we propose a new predistortion scheme with low-rate system identification and Volterra kernel interpolation which allows a drastic cost reduction for the feedback ADC.