To detect and organize trillions of possible volatile molecules, the human olfactory system deploys approximately 3% of the genes in the human genome as olfactory receptors. Our understanding of how the olfactory system organizes the resulting information has many gaps, and relative to other sensory systems, our current ability to measure and reproduce smells is poor. Here we cover the anatomy, circuitry, and psychophysics of olfaction, with an emphasis on the gaps that prevent us from measuring an odor, representing it digitally, and reproducing a perceptual target from a set of sensory primaries.