One especially important feature of metrical music is that it contains periodicities that listeners’ bodily rhythms can adapt to. Recent psychological frameworks have introduced the notion of rhythmic entrainment, among other mechanisms, as an emotion induction principle. In this review paper, we discuss rhythmic entrainment as an affect induction mechanism by differentiating four levels of entrainment in humans—perceptual, autonomic physiological, motor, and social—all of which could contribute to a subjective feeling component. We review the theoretical and empirical literature on rhythmic entrainment to music that supports the existence of these different levels of entrainment by describing the phenomena and characterizing the associated underlying brain processes. The goal of this review is to present the theoretical implications and empirical findings about rhythmic entrainment as an important principle at the basis of affect induction via music, since it rests upon the temporal dimension of music, which is a specificity of music as an affective stimulus.