In order to meet their stringent dependability requirements, most modern packet-switched communication networks support fast-recovery mechanisms in the data plane. While reactions to failures in the data plane can be significantly faster compared to control plane mechanisms, implementing fast recovery in the data plane is challenging, and has recently received much attention in the literature. This survey presents a systematic, tutorial-like overview of packet-based fast-recovery mechanisms in the data plane, focusing on concepts but structured around different networking technologies, from traditional link-layer and IP-based mechanisms, over BGP and MPLS to emerging software-defined networks and programmable data planes. We examine the evolution of fast-recovery standards and mechanisms over time, and identify and discuss the fundamental principles and algorithms underlying different mechanisms. We then present a taxonomy of the state of the art, summarize the main lessons learned, and propose a few concrete future directions.