Are there bi-directional influences between speech perception and music perception? An answer to this question is essential for understanding the extent to which the speech and music that we hear are processed by domain-general auditory processes and/or by distinct neural auditory mechanisms. This review summarizes a large body of behavioral and neuroscientific findings which suggest that the musical experience of trained musicians does modulate speech processing, and a sparser set of data, largely on pitch processing, which suggest in addition that linguistic experience, in particular learning a tone language, modulates music processing. Although research has focused mostly on music on speech effects, we argue that both directions of influence need to be studied, and conclude that the picture which thus emerges is one of mutual interaction across domains. In particular, it is not simply that experience with spoken language has some effects on music perception, and vice versa, but that because of shared domain-general subcortical and cortical networks, experiences in both domains influence behavior in both domains.