Recent years have witnessed an enormous increase in behavioral and neuroimaging studies of numerical cognition. Particular interest has been devoted toward unraveling properties of the representational medium on which numbers are thought to be represented. We have argued that a correct inference concerning these properties requires distinguishing between different input modalities and different decision/output structures. To back up this claim, we have trained computational models with either symbolic or nonsymbolic input and with different task requirements, and showed that this allowed (...) for an integration of the existing data in a consistent manner. In later studies, predictions from the models were derived and tested with behavioral and neuroimaging methods. Here we present an integrative review of this work. (shrink)