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This paper reports on the development of a multi-agent approach to long-term information collection in networks of energy harvesting wireless sensors. In particular, we focus on developing energy management and data routing policies that adapt their behaviour according to the energy that is harvested, in order to maximise the amount of information collected given the available energy budget. In so doing, we introduce a new energy management technique, based on multi-armed bandit learning, that allows each agent to adaptively allocate its energy budget across the tasks of data sampling, receiving and transmitting. By using this approach, each agent can learn the optimal energy budget settings that give it efficient information collection in the long run. Then, we propose two novel decentralised multi-hop algorithms for data routing. The first proveably maximises the information throughput in the network, but can sometimes involve high communication cost. The second algorithm provides near-optimal performance, but with reduced computational and communication costs. Finally, we demonstrate that, by using our approaches for energy management and routing, we can achieve a 120% improvement in long-term information collection against state-of-the-art benchmarks.