Orthogonal frequency division multiplexing (OFDM) is an attractive technique for high-speed data transmission because it has high spectral efficiency and is robust against multipath fading. One main drawback of OFDM systems is the high peak-to-average power ratio (PAPR) at the transmitter’s output. When a high-PAPR OFDM signal passes through a nonlinear device, it may cause in-band distortion and undesired spectral spreading. Selected mapping (SLM) and partial transmit sequence (PTS) schemes are two efficient techniques for reducing the PAPR of OFDM systems. In SLM, the input data block is multiplied by a set of pre-determined phase rotation factors and then passed through a bank of inverse fast Fourier transform (IFFT) units to generate candidate OFDM signals, where the one with the lowest PAPR is selected for transmission. In PTS, the input data block is partitioned into a number of disjoint subblocks using a subblock partition method (SPM), and then the IFFTs of all the subblocks are optimally combined to form a low-PAPR OFDM signal for transmission. Although these two approaches have good PAPR reduction performance, the IFFT computation and/or the optimization process may involve high computational complexity. In this dissertation, we present several methods to alleviate these problems. We first develop a new set of low-complexity conversion matrices (CMs) to simplify the IFFT computation required for the SLM scheme. For an N-subcarrier OFDM system using L times oversampling, the proposed CM-based method uses an LN-point IFFT to generate other LN-point IFFTs (i.e., candidate signals) for the SLM scheme with only 3LN complex additions for each of them. As compared to the conventional SLM scheme, the proposed CM-based method achieves close bit-error-rate (BER) performance with much lower computational complexity but slightly worse PAPR reduction. We then develop a new algorithm to simplify the optimization process of the PTS technique. The proposed PTS scheme uses a cost function to select appropriate samples of each candidate signal for peak power calculation during the optimization process. It achieves almost the same PAPR reduction performance as the conventional PTS scheme, but has much lower computational complexity. We also show that the PTS scheme is a kind of SLM in which the elements of each phase rotation vector are arranged in a pattern determined by the SPM used. Specifically, the elements in the corresponding phase rotation vector are periodic when the PTS scheme uses the interleaved SPM. In this case, the PTS scheme can be realized as SLM by using the proposed low-complexity CM-based method. For the PTS using the adjacent SPM, each subblock of data consists of successive zero elements. Based on this special feature, we develop a mechanism along with an IFFT architecture to avoid trivial computations caused by those zero elements, which can reduce the complexity of the PTS scheme using the adjacent SPM. The existing PAPR reduction methods usually use four times oversampling for the discrete-time OFDM signal to approximate the PAPR of the continuous-time OFDM signal. However, the four times oversampling process increases the computational complexity, especially for those schemes with a large number of IFFT units. To overcome this problem, we propose an efficient method for PAPR estimation of OFDM signals. The proposed method uses an interpolator to find the peak of the four times oversampled OFDM signal around some searched samples of the original discrete-time OFDM signal using oversampling with a factor smaller than four. We also derive some criteria to determine the interpolation filter length and the threshold of sample power for the search process. As compared to the method with four times oversampling, the proposed scheme achieves close PAPR estimation performance with only about half of the computational complexity. It is verified that the proposed PAPR estimation method can successfully be combined with the SLM technique for PAPR reduction.