This article reviews useful postdistortion techniques at the receiver that mitigate distortion caused in the transmitter by clipping and PA nonlinearity. Phase modulation makes PA nonlinearity significantly more challenging for postdistortion compensation compared to clipping noise. TD-based and FD-based techniques, both informed and blind, are reviewed, and novel hybrid techniques in both domains are presented. Statistical techniques are presented that are particularly useful to compensate for PA amplitude compression and clipping. This review highlights the advantages, limitations, tradeoffs and failings of a large number of digital postdistortion (DPoD) techniques and the implementation challenges to overcome.