The ability to segregate and understand speech in complex listening scenarios is an inherent property of the human brain. However, this ability deteriorates as the brain ages. The underlying age-related alteration of neural mechanisms is still unclear. Understanding the subcortical and cortical neural mechanisms of auditory processes might be critical in order to get a better understanding of how they degraded by age. Importantly, the likely non-linearity nature of these auditory processes may conceal important internal mechanisms that might not be captured with traditional linear methodology. This thesis develops a novel non-linear approach based on information theory and investigates the non-linear representation of speech in both the midbrain and the cortex. In this dissertation, midbrain and cortical activities from younger and older listeners are noninvasively recorded with both clean speech (i.e. subjects listening to a single speaker) and with adverse listening conditions (i.e. two competing speakers). Additionally, the effect of informational masking is also investigated. Results from the mutual information analysis suggest an age-related deterioration of the response in the midbrain and a strong effect of the informational masking only in older adults. Conversely, the cortical analysis reveals an exaggerated response in older listeners. Interestingly, this exaggerated response is strongly correlated with behavioral measurements, such as speech-in-noise score and behavioral inhibitory control score. Further analysis also reveals that the exaggerated response in the aging cortex manifests only in the neural representation of the low-frequency speech envelope, while at higher frequencies (60-100 Hz) no differences were seen between younger and older listeners. However, the aging cortex demonstrates neural deficits, at such higher frequency, in suppression of the competing speech in challenging listening conditions, shown by an increasing trend of response level with increasing sound level of the competing speech. In summary, this dissertation develops a novel mutual information approach for analyzing neural recordings, and the results reveal new findings of age-related changes in auditory midbrain and cortical activities.