Recently, it was shown that transceiver hardware impairments have a detrimental impact on the performance of communication systems, especially for high-rate systems. The vast majority of technical contributions in the area of relaying assume ideal transceiver hardware. This paper quantifies the impact of transceiver hardware impairments in dual-hop Amplify-and-Forward (AF) relaying, both for fixed and variable gain relays. The outage probability (OP) in this practical scenario is a function of the instantaneous end-to-end signal-to-noise-and-distortion ratio (SNDR). This paper derives closed-form expressions for the exact and asymptotic OPs under Rayleigh fading, accounting for hardware impairments at both the transmitter and the relay. The performance loss is small at low spectral efficiency, but can otherwise be very substantial. In particular, it turns out that for high signal-to-noise ratio (SNR), the instantaneous end-to-end SNDR converges to a deterministic constant, called the SNDR ceiling, which is inversely proportional to the level of impairments. This stands in stark contrast to the ideal hardware case for which the end-to-end SNDR grows without bound in the high SNR regime.