In-band full-duplex, by which radios may simultaneously transmit and receive over the same channel, has been always considered practically-unfeasible due to the prohibitively strong self-interference. Indeed, a freshly-generated transmit signal power is typically ten orders of magnitude higher than that of a naturally-attenuated received signal. While unable to manage such an overwhelming interference, wireless communications resorted to half-duplex operation, transmitting and receiving over orthogonal channel resources. Recent research has demonstrated the practical feasibility of full-duplexing via successive sophisticated stages of signal suppression/cancellation, bringing this long-held assumption down and reviving the promising full-duplex potentials. Full-duplex relaying (FDR), where intermediate nodes may now support source-destination communication via simultaneous listening/forwarding, represents one of two full-duplex settings currently recommended for deployment in future fifth-generation (5G) systems. Theoretically, it has been widely accepted that FDR potentially doubles the channel capacity when compared to its half-duplex counterpart. Although FDR doubles the multiplexing gain, the effective signal-to-noise ratio (SNR) can be significantly degraded due to the residual self-interference (RSI) if not properly handled. In this work, efficient protocols are devised for different FDR settings. Selective cooperation is proposed for the canonical three-terminal FDR channel with RSI, which exploits the cooperative diversity offered by the independently fading source/relay message replicas arriving at the destination. Closed-form expressions are derived for the end-to-end SNR cumulative distribution function (CDF) under Rayleigh and Nakagami-m fading. Further, the offered diversity gain is presented as a function of the RSI scaling trend with the relay power. We show that the existing diversity problem in simple FDR protocols can be considerably fixed via block transmission with selective cooperation. Beyond the single-relay setting, the outage performance of different opportunistic full-duplex relay selection (FDRS) protocols is also evaluated under Rayleigh and Nakagami-m fading. It is shown that, with state-of-the-art adaptive self-interference cancellation techniques, FDRS can offer the same diversity order of its half-duplex rival while supporting a higher level of spectral efficiency. FDRS is also analyzed when adopted by a spectrum-sharing secondary system while the primary spectrum user imposes an additional interference constraint. Finally, buffer-aided hybrid half-/full-duplex cooperation is addressed. To maximize the end-to-end throughput, joint duplexing mode and link selection is studied where the system leverages the buffer and outage state information at the transmitters. All theoretic findings are corroborated with numerical simulations, with comparisons to existing protocols.