We first briefly summarize data from microelectrode studies on visual maps in non-human primates and other mammals, and characterize differences among the features of the approximately topological maps in the three main sensory modalities. We then explore the almost 50% of human neocortex that contains straightforward topological visual, auditory, and somatomotor maps by presenting a new parcellation as well as a movie atlas of cortical area maps on the FreeSurfer average surface, fsaverage. Third, we review data on moveable map phenomena as well as a recent study showing that cortical activity during sensorimotor actions may involve spatially locally coherent traveling wave and bump activity. Finally, by analogy with remapping phenomena and sensorimotor activity, we speculate briefly on the testable possibility that coherent localized spatial activity patterns might be able to ‘escape’ from topologically mapped cortex during ‘serial assembly of content’ operations such as scene and language comprehension, to form composite ‘molecular’ patterns that can move across some cortical areas and possibly return to topologically mapped cortex to generate motor output there.