The design of compact and reconfigurable radio transceivers with low power consumption and low cost is a challenging task in future wireless communications systems. Transceiver architectures that are amenable to high-level integration will inevitably suffer from various radio frequency (RF) impairments, which limits the communications system performance and hence hinders their wide-spread use in commercial products. In this paper, we present the mitigation of RF impairments as a system identification problem. Four major classes of RF impairments are presented: power amplifier (PA) nonlinearity, in-phase/ quadrature (I/Q) impairments, group delay distortion, and carrier frequency offset and phase noise. Their models and up-todate identification techniques are described here. In particular, various nonlinear signal processing techniques that are effective in mitigating these impairments are also presented here. Theoretical and experimental results show that these mitigation techniques can significantly improve the communications system performance.