Standard analyses of spatial data assume that measurement and prediction locations are measured precisely. In this paper we consider how appropriate methods of estimation and prediction change when this assumption is relaxed and the locations are subject to positional error. We describe basic models for positional error and assess their impact on spatial prediction. Using both simulated data and lead concentration pollution data from Galicia, Spain, we show how the predictive distributions of quantities of interest change after allowing for the positional error, and describe scenarios in which positional errors may affect the qualitative conclusions of an analysis. The subject of positional error is of particular relevance in assessing the exposure of an individual to an environmental pollutant when the position of the individual is tracked using imperfect measurement technology. Copyright © 2010 John Wiley & Sons, Ltd.