Monitoring extreme values (MAX or MIN) is a fundamental problem in wireless sensor networks (and in general, complex dynamic systems). This problem presents very different algorithmic challenges from aggregate and selection queries, in the sense that an individual node cannot by itself determine its inclusion in the query result. We present novel query processing algorithms for this problem, with the goal of minimizing message traffic in the network. These algorithms employ a hierarchy of local constraints, or thresholds, to leverage network topology such that message-passing is localized. We evaluate all algorithms using simulated and real-world data to study various trade-offs. Copyright 2006 ACM.