Received power measurements at spatially distributed monitors can be usefully exploited to deduce various characteristics of active wireless transmitters. In this paper, we study the problem of “blind” estimation of a wireless node's transmit power utilizing solely received power measurements at spatially distributed monitors, without any prior knowledge about the transmitter's location or any statistical characterization of its transmit power. We first consider a deterministic setup and utilize a geometrical approach to obtain fundamental limitations on estimating the transmit power and location of an unknown wireless node. We show that a regular placement of monitors, though appealing, does not provide sufficient measurement diversity to yield a unique estimate. We then extend the setup to consider wireless fading and present a theoretical analysis of maximum likelihood (ML) estimate, which is analytically shown to be asymptotically optimal. Finally, we provide numerical results comparing the performance of the estimator through simulations and on a dataset of field measurements.