We investigated neural mechanisms that support voice recognition in a training paradigm with fMRI. The same listeners were trained on different weeks to categorize the mid-regions of voice-morph continua as an individual's voice. Stimuli implicitly defined a voice-acoustics space, and training explicitly defined a voice-identity space. The predefined centre of the voice category was shifted from the acoustic centre each week in opposite directions, so the same stimuli had different training histories on different tests. Cortical sensitivity to voice similarity appeared over different time-scales and at different representational stages. First, there were short-term adaptation effects: Increasing acoustic similarity to the directly preceding stimulus led to haemodynamic response reduction in the middle/posterior STS and in right ventrolateral prefrontal regions. Second, there were longer-term effects: Response reduction was found in the orbital/insular cortex for stimuli that were most versus least similar to the acoustic mean of all preceding stimuli, and, in the anterior temporal pole, the deep posterior STS and the amygdala, for stimuli that were most versus least similar to the trained voice-identity category mean. These findings are interpreted as effects of neural sharpening of long-term stored typical acoustic and category-internal values. The analyses also reveal anatomically separable voice representations: one in a voice-acoustics space and one in a voice-identity space. Voice-identity representations flexibly followed the trained identity shift, and listeners with a greater identity effect were more accurate at recognizing familiar voices. Voice recognition is thus supported by neural voice spaces that are organized around flexible ‘mean voice’ representations.