This mini review is aimed at a clinician-scientist seeking to understand the role of oscillations in neural processing and their functional relevance in speech and music perception. We present an overview of neural oscillations, methods used to study them, and their functional relevance with respect to music processing, aging, hearing loss, and disorders affecting speech and language. We first ... [Show full abstract] review the oscillatory frequency bands and their associations with speech and music processing. Next we describe commonly used metrics for quantifying neural oscillations, briefly touching upon the still-debated mechanisms underpinning oscillatory alignment. Following this, we highlight key findings from research on neural oscillations in speech and music perception, as well as contributions of this work to our understanding of disordered perception in clinical populations. Finally, we conclude with a look toward the future of oscillatory research in speech and music perception, including promising methods and potential avenues for future work. We note that the intention of this mini review is not to systematically review all literature on cortical tracking of speech and music. Rather, we seek to provide the clinician-scientist with foundational information that can be used to evaluate and design research studies targeting the functional role of oscillations in speech and music processing in typical and clinical populations.