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In this survey we review energy-aware routing protocols for wireless multihop ad hoc networks and critically discuss the main results in this area. The classification presented is in no case unique but summarizes the chief characteristics of the many published proposals for energy conservation. A common pitfall detected in most of the studies is the lack of unambiguous notion of network's lifetime and hence of clear objective of the designed algorithm. We, therefore, define first what operational lifetime for ad hoc networks means and then analyze the achievements from that angle. After getting insight into the different energy-aware routing protocols we point out another approach for extending network's operational lifespan, which has been overlooked in the relevant literature.