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In this paper, we consider a simple network consisting of a source, a half-duplex decode-and- forward relay, and a destination. In contrast to most of the existing literature, we assume that the relay is equipped with a buffer and show that this can lead to substantial performance gains. We propose a simple protocol which chooses either the source-relay or the relay-destination link for transmission depending on the instantaneous channel state information. For this simple protocol, we derive the throughput for adaptive rate transmission and the outage probability for fixed rate transmission. Our results show that, unlike conventional relaying, buffer-aided relaying yields a diversity gain of two. In addition, throughput gains of up to 100 % compared to conventional relaying are possible.