The next-generation (5G/6G) wireless communication aims to leapfrog the currently occupied sub-6 GHz spectrum to the wideband millimeter-wave (MMW) spectrum. However, MMW spectrums with high-order modulation schemes drive the power amplifier (PA) at significant back-off, causing severe nonlinear distortions, thus deteriorating the transceiver's (TRXs) modulation process. Typically, the TRX efficacy is quantified with standardized linearization matrices, which take advantage of different predistortion (PD) schemes to handle deep compression of the PA. In this regard, TRX baseband signals are mostly linearized in the digital domain, where digitally controlled linearization needs higher sampling rates due to increasing MMW bandwidths to compensate for intermodulation (IMD) products, resulting in increased system cost and power consumption. Alternately, the digitally controlled analog-based linearization, i.e., the hybridization of digital predistortion (DPD) and analog predistortion (APD), is highly productive and cost-effective for fulfilling the linearized energy-efficient design vision of MMW networks. Therefore, this paper puts an extensive spotlight on the progress in PD-based linearization for 5G and beyond communications. It first provides background information on the advancements of PD schemes through recent surveys, then classifies the general roadmap of PD waveform processing across the TRX system models as preliminary. After this, we present three prominent PD architectures and their design approaches with intrinsic performance metrics. Finally, we explore four case studies encompassing PD operation under certain nonlinear constraints of different communication schemes. We examine the suitability of PD-based linearization solutions, both existing and proposed till the first quarter of 2022, and identify the potential prospects in this domain.