Under scenarios of high mobility, the traditional coherent demodulation schemes (CDS) have a limited performance, due to the fact that reference signals cannot effectively track the variations of the channel with an affordable overhead. As an alternative solution, non--coherent demodulation schemes (NCDS) based on differential modulation have been proposed. Even in the absence of reference signals, they are capable of outperforming the CDS with a reduced complexity. The literature on NCDS laid the theoretical foundations for simpliϔied channel and signal models, often single--carrier and spatially uncorrelated flat--fading channels. In this work, the most recent results assuming orthogonal frequency division multiplexing (OFDM) signaling and realistic channel models are explained, and the impact of some hardware impairments such as the phase noise (PN) and the non--linear high power amplifier (HPA) are also considered. Moreover, new potential research lines are also highlighted.