A challenging goal in neuroscience is to be able to read out, or decode, mental content from brain activity. Recent functional magnetic resonance imaging (fMRI) studies have decoded orientation, position and object category from activity in visual cortex. However, these studies typically used relatively simple stimuli (for example, gratings) or images drawn from fixed categories (for example, faces, houses), and decoding was based on previous measurements of brain activity evoked by those same stimuli or categories. To overcome these limitations, here we develop a decoding method based on quantitative receptive-field models that characterize the relationship between visual stimuli and fMRI activity in early visual areas. These models describe the tuning of individual voxels for space, orientation and spatial frequency, and are estimated directly from responses evoked by natural images. We show that these receptive-field models make it possible to identify, from a large set of completely novel natural images, which specific image was seen by an observer. Identification is not a mere consequence of the retinotopic organization of visual areas; simpler receptive-field models that describe only spatial tuning yield much poorer identification performance. Our results suggest that it may soon be possible to reconstruct a picture of a person's visual experience from measurements of brain activity alone.