Abstract-Opportunistic networks are a class of mobile ad hoc networks (MANETs) where contacts between mobile nodes occur unpredictably and where a complete end-to-end path between source and destination rarely exists at one time. Two important functions, traditionally provided by the transport layer, are ensuring the reliability of data transmission between source and destination, and ensuring that the network does not become congested with traffic. However, modified versions of TCP that have been proposed to support these functions in MANETs are ineffective in opportunistic networks. In addition, opportunistic networks require different approaches to those adopted in the more common intermittently connected networks, e.g. deep space networks. In this article we capture the state of the art of proposals for transfer reliability and storage congestion control strategies in opportunistic networks. We discuss potential mechanisms for transfer reliability service, i.e. hop-by-hop custody transfer and end-to-end return receipt. We also identify the requirements for storage congestion control and categorise these issues based on the number of message copies distributed in the networks. For single-copy forwarding, storage congestion management and congestion avoidance mechanism are discussed. For multiple-copy forwarding, the principal storage congestion control mechanisms are replication management and drop policy. Finally, we identify open research issues in the field where future research could usefully be focused.