Understanding the neural mechanisms of invariant object recognition remains one of the major unsolved problems in neuroscience. A common solution that is thought to be employed by diverse sensory systems is to create hierarchical representations of increasing complexity and tolerance. However, in the mammalian auditory system many aspects of this hierarchical organization remain undiscovered, including the prominent classes of high-level representations (that would be analogous to face selectivity in the visual system or selectivity to bird's own song in the bird) and the dominant types of invariant transformations. Here we review the recent progress that begins to probe the hierarchy of auditory representations, and the computational approaches that can be helpful in achieving this feat.