Linearization of millimeter-wave (mmW) phased arrays is one of the key enablers for improving the system performance in terms of power, efficiency and linearity. However, phased array transceiver topologies that have multiple parallel nonlinear components with a shared digital input challenge the standard digital predistortion techniques. In addition, different analogue beamforming techniques complicate the linearization even further due to the fact that the signal nonlinearity has to be observed or modelled over-the-air (OTA) together with the impacts of antennas and even the directive mmW radio channel. The best linearization strategy depends on the system level targets of linearity such as error vector magnitude and adjacent channel power ratio which have slightly different nature when observed in the radiated far-field. In this paper, we present our view and the status of the literature on the topic of phased array digital predistortion. We highlight that the nonlinear distortion have a beam shape which may be different from the linear part of the beam. We also review the antenna array figures of merit describing the nonlinearity. Finally, we show an experimental example of OTA linearization of a 28 GHz phased array transmitter.