Smells are psychologically experienced and neuroanatomically represented in a compositional format that offers a new theoretical access point to a host of central issues within the chemical senses and cognitive neuroscience more broadly. The talk begins with a brief overview of the concept of compositionality, the forms that it might take, and its importance for theories of mental architecture. Drawing upon recent neuroscientific and behavioral experimental findings, the talk then shows that olfaction employs a functionally compositional format that is incompatible with the compositional format of our conceptual and semantic processes. Recognizing that olfaction implements a compositional format that is incompatible with the format employ by conceptual and semantic cortical processing centers provides an explanation of the puzzling discrepancy between our gifted ability to discriminate odors, yet poor capacity to name smells. Building upon this theory of the format of smell, the talk proceeds to highlight the theory’s explanatory power for other olfactory phenomena such as odor navigation, how to individuate the chemical senses, and the olfactory memory bump. The talk concludes by suggesting how studying the format of smell provides the impetuous for a new approach to a range of topics in cognitive neuroscience, and in particular debates concerning our mental architecture.