The mammalian brain commonly uses structural proximity to reflect proximity in stimulus and perceptual space. Objects or object features that are near each other in physical structure or perception are also near each other in the brain. This generates sensory maps. The topography of olfactory connectivity implies a rudimentary map in the olfactory epithelium, a more intricate map in the olfactory bulb, but no ordered topography is evident in piriform cortex. Currently, we are largely unable to link the ordered topography in epithelium and bulb to meaningful olfactory axes within a strong predictive framework. We argue that the path to uncovering such a predictive framework depends on systematically characterizing olfactory perception, and we describe initial efforts in this direction.