As newly proposed end-to-end, store-and-forward networks, delay and disruption tolerant networks (DTN) are characterized by intermittent connectivity, frequent partitions, extremely high latency, asymmetric data rates, high error rates, heterogeneous interconnection, etc. Hence, traditional routing protocols for Internet, mobile ad hoc networks and wireless sensor networks, are difficult to be applied efficiently in DTN scenarios, and routing in DTN faces many new challenges. After briefly describing the fundamental characteristics of DTN and the major challenges in designing routing protocols, the metrics used to evaluate the DTN routing protocols are proposed. Next, research on routing protocols for DTN is comprehensively summarized and deeply analyzed in this paper, including unicast routing, multicast routing, and anycast routing. Finally, the main routing protocols are compared, and the open issues for the future research are also pointed out to motivate new research and development in the field of DTN.