When we have a rich and vivid memory for a past experience, it often feels like we are transported back in time to witness once again this event. Indeed, a perfect memory would exactly mimic the experiential quality of direct sensory perception. We used fMRI and multivoxel pattern analysis to map and quantify the similarity between patterns of activation evoked by direct perception of a diverse set of short video clips and the vivid remembering, with closed eyes, of these clips. We found that the patterns of distributed brain activation during vivid memory mimicked the patterns evoked during sensory perception. Using whole-brain patterns of activation evoked by perception of the videos, we were able to accurately classify brain patterns that were elicited when participants tried to vividly recall those same videos. A discriminant analysis of the activation patterns associated with each video revealed a high degree (explaining over 80% of the variance) of shared representational similarity between perception and memory. These results show that complex, multifeatured memory involves a partial reinstatement of the whole pattern of brain activity that is evoked during initial perception of the stimulus.