Music has strong emotional powers. How are we to understand affective responses to music? What does music teach us about emotions? Why are musical emotions important? Despite the rich literature in philosophy and the empirical sciences, particularly psychology and neuroscience, little attention has been paid to integrating these approaches. This extensive review aims to redress this imbalance and establish a mutual dialogue between philosophy and the empirical sciences by presenting the main philosophical puzzles from an affective science perspective. The chief (...) problem is contagion. Sometimes, listeners perceive music as expressing some emotion and this elicits the same emotion in them. Contagion is perplexing because it collides with the leading theory of emotions as experiences of values. This article mostly revolves around the critical presentation of the philosophical solutions to this problem in light of recent developments in emotion theory and affective science. It also highlights practical issues, particularly the role of musical emotions in well-being and health, by tackling the paradox of sad music, i.e., the question of why people enjoy sad music. It thus bridges an important gap between theoretical and real-life issues as well as between philosophical and empirical investigations on affective responses to music. (shrink)