Advances in wireless communication and microelectronics have led to the development of low-power compact sensor nodes (popularly called motes) that are capable of sensing, computing, and communication. A large number of these nodes can be deployed over some area of interest to form a multi-hop network, commonly referred to as a wireless sensor network (WSN). Typical applications of WSNs include, environment and process monitoring in industrial installations, forest fire detection, structural health monitoring, etc. In such applications where the variables to be measured are slowly varying, or the events to be monitored are rare, continuous sensing is unnecessary. Instead, the nodes, in order to conserve their battery power, can sleep-wake cycle whereby each node is allowed to independently alternate between an ON state and a low power OFF state. Sleep-wake cycling, while increasing the network lifetime, renders the network disconnected a large fraction of the time; however, connectivity can be established over time by transporting packets in a store-and-forward manner, whereby packets are held by a forwarding node until a suitable node wakes up in its neighborhood that can serve to forward the packet towards the destination. We are concerned with sleep-wake cycling multi-hop wireless networks whose main task is to carry sporadic alarms packets from sensing nodes to a sink node. Our objective is to design simple local-information based routing solutions for such networks. With this in mind, we propose a relay selection problem that arises at a forwarding node (which is currently holding the alarm packet) while choosing a next-hop relay node. The forwarder, as and when the relays wake-up, evaluating the goodness of a relay based on a “reward” metric (e.g., a function of the relay’s progress towards sink, and the power required to get the packet across), has to decide whether to forward to this relay or to wait for future ones (i.e., to stop or continue). The forwarder’s objective is to choose a relay so as to minimize a combination of the average delay incurred and the average reward achieved. A basic version of our relay selection problem is equivalent to the basic asset selling problem studied in the operations research literature. After reviewing the solution to the basic problem we will proceed to study a model with full information, referred to as the completely observable (CO) model, where the number of relays is exactly known to the forwarder. Formulating the problem as a Markov decision process (MDP) we will characterize the solution to the CO model in terms of recursively-computable threshold functions. Next, we consider the partially observable (PO) model where only a belief (probability mass function) on the number of relays is known. Hence, the PO model falls within the realm of partially observable MDPs. After incorporating our model into this framework we will characterize the solution in terms of stopping sets, which is the set of all belief states where it is optimal to stop. Our main contribution here is to obtain inner and outer bounds for the stopping sets. We next propose a variant where the relays, upon waking up, do not reveal their rewards immediately, but instead the forwarder can choose to probe the relay to know its reward, incurring a probing cost. Thus, to the existing set of stop and continue actions, we have added a new probe action. This model is motivated by the efforts required to learn the channel gains (by probing) in a wireless system. A key result we prove here is that the solution is characterized in terms of stage independent thresholds. Finally, we study a model comprising two forwarders which are competing against each other to choose a next-hop relay (one for each). Here, a relay is allowed to offer possibly different reward to each forwarder. We will first consider a complete information case where the reward pair of a relay is known to both the forwarders. Using stochastic game theory we will characterize the solution to this model in terms of Nash equilibrium policy pairs (NEPPs). We obtain results illustrating the structure of NEPPs. Next, we study a partial information model where each forwarder gets to observe only its reward value. Towards obtaining the solution for this model, we will first formulate a Bayesian game which is effectively played by both the forwarders at each stage. Next, for this Bayesian game we prove the existence of Nash equilibrium strategies within the class of threshold strategies. This result will enable us to construct NEPPs for the partial information model. Although our primary contribution from the thesis is the theoretical study of the above mentioned variants of the basic relay selection model, we have also conducted extensive simulations to study the end-to-end performance obtained by applying the solution to these models at each hop en-route to the sink in a sleep-wake cycling WSN.