Multicarrier transmission schemes produce time‐domain (TD) signals with large envelope fluctuations. These signals suffer from nonlinear distortions when passing through a high‐power amplifier (HPA) because of its nonlinear transfer function. Several metrics are used to quantify the envelope fluctuations: peak‐to‐average power ratio (PAPR), crest factor (CF), and cubic metric (CM). Multiple techniques and algorithms have been proposed for reducing such metrics in the literature. This article reviews all the possible PAPR reduction techniques and emphasizes the importance of their application in multicarrier schemes. Besides, new variants adapted to multiple‐input multiple‐output (MIMO) orthogonal frequency division multiplexing (OFDM) are also presented, which take on importance in 5G systems. Finally, a comparison among these techniques is presented in terms of the key aspects considered when designing a 5G system: power increase, implementation complexity, bit error rate (BER) degradation, and required side information. It is shown that the selection of the PAPR reduction technique depends on the application, the system requirements, and the scenario.