Cognitive radio networks (CRNs) have emerged as a promising solution to enhance spectrum utilization by using unused or less used spectrum in radio environments. The basic idea of CRNs is to allow secondary users (SUs) access to licensed spectrum, under the condition that the interference perceived by the primary users (PUs) is minimal. In CRNs, the channel availability is uncertainty due to the existence of PUs, resulting in intermittent communication. Transmission control protocol (TCP) performance may significantly degrade in such conditions. To address the challenges, some transport protocols have been proposed for reliable transmission in CRNs. In this paper we survey the state-of-the-art transport protocols for CRNs. We firstly highlight the unique aspects of CRNs, and describe the challenges of transport protocols in terms of PU behavior, spectrum sensing, spectrum changing and TCP mechanism itself over CRNs. Then, we provide a summary and comparison of existing transport protocols for CRNs. Finally, we discuss several open issues and research challenges. To the best of our knowledge, our work is the first survey on transport protocols for CRNs.