This article presents an overview of the major trends and challenges involved with the design of multi-band, multi-standard digitally-intensive radio frequency transceivers for next generation mobile communications. In addition, we discuss in detail one aspect of the implementation challenges, namely the occurrence and cancellation of self-interference especially in carrier aggregation modes. For that, we present a novel digital cancellation technique to jointly compensate the self-interference caused by transmit (Tx) modulated spurs and Tx second order intermodulation distortion products (IMD2) in the receiver. This architecture exploits the underlying relation between both types of interference and offers a low-complexity solution to mitigate the Tx-IMD2 interference. Simulation results show, that the proposed technique significantly suppresses both types of interference and restores the signal-to-noise ratio of the wanted signal within 0.3 dB from its value in the absence of interference, thereby achieving 30 dB of cancellation.