The delay tolerant network has been extensively studied and applied in recent years. When there is continuing and stable end-to-end path between the source node and the destination node in DTN, the traditional TCP/IP based network routing protocols cannot be applied to Delay/Disruption Tolerant Network. The storage-forward policy is used for message transmission. The performance of DTN routing protocols is influenced by the link existent time, buffer size of the nodes, and the mobility mode of the network. This paper discusses the study of DTN routing protocols, compare their performance, and highlight the future trends of DTN routing protocols.