In this talk, we introduce a few stochastic scheduling, estimation, and resource allocation problems in wireless networks.  The common theme is energy efficiency; however, energy can be conserved in a number of different ways. One way is by limiting the idle time of a node's radio.  A first cause of such idle time is not having any data to transmit, a factor we explore in a single node sleep scheduling problem.  A second cause is a lack of synchronization; i.e., the node has data to transmit, but the receiver is not listening.  Accordingly, we consider the problem of calibrating an ultra-low power clock (1 pW) of a sensor node, by dynamically scheduling temperature measurements.  Because the clock accuracy is temperature-dependent, these measurements can be used in combination with the local clock time to obtain a more accurate estimate of elapsed real time, thus improving synchronization.  Next, we consider the problem of designing an adaptive sampling strategy for a network of sensors that measures soil moisture profiles.  In-situ measurements are used to calibrate and validate measurements from satellite radars and radiometers that allow global mapping, but have a coarse resolution.  By controlling when and where soil moisture measurements are taken, we can reduce the workload on the network and conserve energy.  Finally, one can also conserve energy via transmission scheduling, by exploiting the temporal and spatial variation of the wireless channel.  We examine this possibility in the context of a wireless media streaming problem, where strict underflow constraints play a key role.