This article presents novel solutions for suppressing passive intermodulation (PIM) distortion in frequency-division duplexing (FDD)-based radio transceivers, stemming from nonlinear radio frequency (RF) components and simultaneous transmission and reception, with special emphasis on modern carrier aggregation networks. With certain transmission band combinations in, e.g., long-term evolution (LTE) or the emerging 5G new radio (NR) mobile radio systems, the nonlinear distortion produced by the passive components of the transceiver RF front end can result in intermodulation (IM) distortion that falls within one of the configured reception bands. While the traditional solution to mitigate this problem is to reduce the transmit power, we take an alternative approach and seek to cancel such PIM in the transceiver digital front end by using the original transmit data as a reference. To generate as accurate cancellation signal as possible, we derive different advanced signal models for the observable IM distortion at own receiver band that incorporates also the power amplifier (PA) nonlinearities, together with the passive component nonlinearities and the frequency-selective responses of the duplex filters. The performance and the processing complexity of the devised digital cancellation and parameter estimation solutions are evaluated with real-life RF measurements, where an actual LTE-Advanced user equipment (UE)-type transceiver system is utilized. The obtained results show that the proposed cancellers are implementation feasible and can suppress the self-interference by over 20 dB, canceling the distortion nearly perfectly up to UE transmit powers of +24 dBm. The results also indicate that, in many cases, it is necessary to model the nonlinear distortion effects produced by the PAs, even if the individual component carriers are combined after the amplification stage.