In this paper, we investigate the fading two-hop full-duplex (FD) relay channel with self-interference, which is comprised of a source, an FD relay impaired by self-interference, and a destination, where a direct source-destination link does not exist. For this channel, we propose three buffer-aided relaying schemes with adaptive reception-transmission at the FD relay for the cases when the source and the relay both perform adaptive-rate transmission with adaptive-power allocation, adaptive-rate transmission with fixed-power allocation, and fixed-rate transmission, respectively. The proposed buffer-aided relaying schemes enable the FD relay to adaptively select to either receive, transmit, or simultaneously receive and transmit in a given time slot based on the qualities of the receiving, transmitting, and self-interference channels; a degree-of-freedom unavailable without buffer-aided relaying. Our numerical results show that significant performance gains are achieved using the proposed buffer-aided relaying schemes compared to conventional FD relaying, where the FD relay is forced to always simultaneously receive and transmit, and to buffer-aided half-duplex relaying, where the half-duplex relay cannot simultaneously receive and transmit. The main implication of this work is that FD relaying systems without buffer-aided relaying miss-out on significant performance gains.