In this paper, we investigate the two-hop full-duplex (FD) relay channel with self-interference and fading, which is comprised of a source, an FD relay, and a destination, where a direct source-destination link does not exist and the FD relay is impaired by self-interference. 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-power allocation, fixed-power allocation, and fixed-rate transmission, respectively. The proposed buffer-aided relaying schemes significantly improve the achievable rate and the throughput of the considered relay channel by enabling 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. 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.