The auditory cortex is essential for encoding complex and behaviorally relevant sounds. Many questions remain concerning whether and how distinct cortical neuronal subtypes shape and encode both simple and complex sound properties. In chapter 2, we tested how neurons in the auditory cortex encode water-like sounds perceived as natural by human listeners, but that we could precisely parametrize. The stimuli exhibit scale-invariant statistics, specifically temporal modulation within spectral bands scaled with the center frequency of the band. We used chronically implanted tetrodes to record neuronal spiking in rat primary auditory cortex during exposure to our custom stimuli at different rates and cycle-decay constants. We found that, although neurons exhibited selectivity for subsets of stimuli with specific statistics, over the population responses were stable. These results contribute to our understanding of how auditory cortex processes natural sound statistics. In chapter 3, we review studies examining the role of different cortical inhibitory interneurons in shaping sound responses in auditory cortex. We identify the findings that support each other and the mechanisms that remain unexplored. In chapter 4, we tested how direct feedback from auditory cortex to the inferior colliculus modulated sound responses in the inferior colliculus. We optogenetically activated or suppressed cortico-collicular feedback while recording neuronal spiking in the mouse inferior colliculus in response to pure tones and dynamic random chords. We found that feedback modulated sound responses by reducing sound selectivity by decreasing responsiveness to preferred frequencies and increasing responsiveness to less preferred frequencies. Furthermore, we tested the effects of perturbing intra-cortical inhibitory-excitatory networks on sound responses in the inferior colliculus. We optogenetically activated or suppressed parvalbumin-positive (PV) and somatostatin-positive (SOM) interneurons while recording neuronal spiking in mouse auditory cortex and inferior colliculus. We found that modulation of neither PV- nor SOM-interneurons affected sound-evoked responses in the inferior colliculus, despite significant modulation of cortical responses. Our findings imply that cortico-collicular feedback can modulate responses to simple and complex auditory stimuli independently of cortical inhibitory interneurons. These experiments elucidate the role of descending auditory feedback in shaping sound responses. Together these results implicate the importance of the auditory cortex in sound processing.