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Sleep scheduling is a widely used strategy for saving the energy of sensor nodes and prolonging the lifetime of a wireless sensor network (WSN). The lower the duty cycle is, the longer the network lifetime will be. However, sleep scheduling brings great challenges to the design of efficient distributed routing protocols for multi-hop duty-cycled WSNs. This issue has attracted much attention and various routing protocols have been proposed. In this article we first summarize the fundamental issues in the design of routing protocols for such networks, and then classify existing protocols based on different design criteria. We then present a survey of state-of-the-art routing protocols in this area. We illustrate how different protocols work and discuss their merits and deficiencies. Finally, we point out some future directions for routing in duty-cycled wireless sensor networks.