A prominent application of Wireless Sensor Networks is the monitoring of physical phenomena. The value of the monitored attributes naturally depends on the accuracy of the spatial sampling achieved by the deployed sensors. The monitored phenomena often tend to have unknown spatial distributions at pre-deployment stage, which also change over time. This can detrimentally affect the overall achievable accuracy of monitoring. Consequently, reaching an optimal (accuracy driven) static sensor node deployment is generally not possible, resulting in either under- or over-sampling of signals in space. Our goal is to provide for adaptive spatial sampling. The key challenges consist in identifying the regions of over- or under-sampling and in suggesting the appropriate countermeasures. In this paper, we propose a Voronoi based adaptive spatial sampling (ASample) solution. Our approach removes unnecessary samples from regions of over-sampling and generates additional new sampling locations in the under-sampling regions to fulfill specified accuracy requirements. Simulation results show that ASample significantly and efficiently reduces the mean square error of the achieved measurement accuracy. © 2010 IEEE.