The capacity of the auditory system to extract spatial information relies principally on the detection and interpretation of binaural cues, i.e., differences in the time of arrival or level of the sound between the two ears. In this review, we consider the effects of unilateral or asymmetric hearing loss on spatial hearing, with a focus on the adaptive changes in the brain that may help to compensate for an imbalance in input between the ears. Unilateral hearing loss during development weakens the brain's representation of the deprived ear, and this may outlast the restoration of function in that ear and therefore impair performance on tasks such as sound localization and spatial release from masking that rely on binaural processing. However, loss of hearing in one ear also triggers a reweighting of the cues used for sound localization, resulting in increased dependence on the spectral cues provided by the other ear for localization in azimuth, as well as adjustments in binaural sensitivity that help to offset the imbalance in inputs between the two ears. These adaptive strategies enable the developing auditory system to compensate to a large degree for asymmetric hearing loss, thereby maintaining accurate sound localization. They can also be leveraged by training following hearing loss in adulthood. Although further research is needed to determine whether this plasticity can generalize to more realistic listening conditions and to other tasks, such as spatial unmasking, the capacity of the auditory system to undergo these adaptive changes has important implications for rehabilitation strategies in the hearing impaired.