In this paper we introduce coverage maps as a new way of representing the environment of a mobile robot. Coverage maps store for each cell of a given grid a posterior about the amount the corresponding cell is covered by an obstacle. Using this representation a mobile robot can more accurately reason about its uncertainty in the map of the environment than with standard occupancy grids. We present a model for proximity sensors designed to update coverage maps upon sensory input. We also describe how coverage maps can be used to formulate a decision-theoretic approach for mobile robot exploration. We present experiments carried out with real robots in which accurate maps are build from noisy ultrasound data. Finally, we present a comparison of different view-point selection strategies for mobile robot exploration.