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In olfactory systems, convergence of sensory neurons onto glomeruli generates a map of odorant receptor identity. How glomerular maps relate to sensory space remains unclear. We sought to better characterize this relationship in the mouse olfactory system by defining glomeruli in terms of the odorants to which they are most sensitive. Using high-throughput odorant delivery and ultrasensitive imaging of sensory inputs, we imaged responses to 185 odorants presented at concentrations determined to activate only one or a few glomeruli across the dorsal olfactory bulb. The resulting datasets defined the tuning properties of glomeruli - and, by inference, their cognate odorant receptors - in a low-concentration regime, and yielded consensus maps of glomerular sensitivity across a wide range of chemical space. Glomeruli were extremely narrowly tuned, with ~25% responding to only one odorant, and extremely sensitive, responding to their effective odorants at sub-picomolar to nanomolar concentrations. Such narrow tuning in this concentration regime allowed for reliable functional identification of many glomeruli based on a single diagnostic odorant. At the same time, the response spectra of glomeruli responding to multiple odorants was best predicted by straightforward odorant structural features, and glomeruli sensitive to distinct odorants with common structural features were spatially clustered. These results define an underlying structure to the primary representation of sensory space by the mouse olfactory system.