We introduce two conceptual models for wireless sensing and control with power-limited sensors and controllers. The limited battery power of the wireless device is captured in the models by imposing hard constraints on either the number of available transmissions the device can make, or on the number of cycles it can stay awake. Such hard constraints can be viewed as a measurement budget, under which estimation or control policies will have to be developed over a given decision horizon. Among the two representative models studied here, the first one is one of optimal scheduling of a finite measurement budget for a Gauss-Markov process over an observation horizon. The second one is an optimal estimation problem where the number of transmissions the wireless sensor can make is limited to a number, M, which is less than the observation horizon, N. It is shown that both problems can be solved by employing dynamic-programming type arguments, and their solutions have a threshold characterization.