Abstract-Orthogonal frequency division multiplexing (OFDM) is a robust and reliable multicarrier modulation scheme that has proven to be adequate for broadband communications. It is widely used in broadcasting and broadband wireless and wireline systems. However, in scenarios where the communication devices are power-limited, such as mobile and satellite communications, OFDM has not been massively used or even not used at all. For instance, OFDM is used only in downlink of 4G networks, while the uplink uses single carrier frequency division multiplexing. One of the main culprits of this is the high peak to average power ratio (PAPR) of the OFDM signal. Reducing the PAPR of the OFDM signals is important for a large variety of application. Several PAPR reduction techniques for OFDM have been proposed recently. The aim of this paper is to present a tutorial about a set of algorithms based on Walsh-Hadamard transform (WHT) for reducing the PAPR of the OFDM symbols. We also propose a new technique, named selective mapping based on WHT without extended information (SLM-WHT-WEI), which does not convey the explicit information to the receiver. We will show that the approaches based on WHT can also improve the OFDM symbol error rate performance over frequency-selective channels. Different schemes based on the properties of the WHT are presented and compared, assuming linear and non-linear channels. The PAPR reduction performance analysis shows that the PAPR can be effectively reduced while good performance in terms of symbol error rate can be achieved even in severely constrained channel conditions.