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Computational models are increasingly essential to systems neuroscience. Models serve as proofs of concept, tests of sufficiency, and as quantitative embodiments of working hypotheses and are important tools for understanding and interpreting complex data sets. In the olfactory system, models have played a particularly prominent role in framing contemporary theories and presenting novel hypotheses, a role that will only grow as the complexity and intricacy of experimental data continue to increase. This review will attempt to provide a comprehensive, functional overview of computational ideas in olfaction and outline a computational framework for olfactory processing based on the insights provided by these diverse models and their supporting data.