While the study of music perception and cognition (from a psychological perspective) spans several decades, the cognitive neuroscience of music has grown substantially in recent years. Like the field of neuroaesthetics more broadly, music cognition is a highly interdisciplinary field, with researchers from diverse backgrounds including music theory, neuroscience, cognitive science, and music therapy, among others. In this chapter, we discuss music in terms of its component parts and focus on neuroscientific findings related to these. Specifically, we discuss foundational and recent work investigating cognitive and neural systems underlying pitch, tonality, timbre, and rhythm and conclude with a final section on affective responses to music. While discussing music in this way is inherently reductionist (see our final section on “Major Challenges, Goals, and Suggestions”), understanding the basic components of music, and how listeners respond to them, sets an important foundation for future work seeking to understand listeners’ aesthetic responses to music.