In this talk, we address the critical issues related to nonlinear amplifier problems in wireless communications and the developments in multiple access techniques to face these issues and increase power efficiency. First of all, we review the Orthogonal Frequency-Division Multiplexing (OFDM) vs. Single-Carrier Transmission with Frequency-Domain Equalization (SC-FDE) issue, which first came up in Digital Audio and Video Broadcasting and continued later in wireless communications. Then, we discuss the birth and the principle of Orthogonal Frequency-Division Multiple Access (OFDMA) and of Single-Carrier Frequency-Division Multiple Access (SC-FDMA) and compare these multiple access techniques in a cellular environment using the Long-Term Evolution (LTE) standard and assuming a linear channel. Finally, we give a comprehensive presentation of the effect of nonlinear power amplifiers on the transmitted signal and the methods used to compensate for the resulting distortion. A comparison is then made between OFDMA and SC-FDMA using nonlinear power amplifiers. Our analysis indicates that OFDMA performs better on linear channels, particularly with high-level signal constellations, but that SC-FDMA reduces high-power amplifier back-off by 1.5 – 2.0 dB. The final conclusion in that it is better to use OFDMA for users close to the base station in order to increase cell capacity, and in contrast it is better to use SC-FDMA for users near the cell edge to increase the cell range.