Olfactory stimuli are encountered across a wide range of odor concentrations in natural environments. Defining the neural computations that support concentration invariant odor perception, odor discrimination, and odor-background segmentation across a wide range of stimulus intensities remains an open question in the field. In principle, adaptation could allow the olfactory system to adjust sensory representations to the current stimulus conditions, a well-known process in other sensory systems. However, surprisingly little is known about how adaptation changes olfactory representations and affects perception. Here we review the current understanding of how adaptation impacts processing in the first two stages of the vertebrate olfactory system, olfactory receptor neurons (ORNs), and mitral/tufted cells.