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We review the models from a 50-year perspective on the work that has challenged, supported, and extended the original proposal that these interactions mediate both lateral inhibition and oscillatory activity, essential steps in the neural basis of olfactory processing and perception. We highlight strategies behind the neurophysiological experiments and the Rall methods that enhance the ability of detailed compartmental modeling to give counterintuitive predictions that lead to deeper insights into neural organization at the synaptic and circuit level. 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