To investigate the modularity of language processing and, specifically, the question of whether the language module is informationally encapsulated, many experiments examined the impact of music expertise and music training on the language system (phonology, semantics and syntax). Finding positive evidence would argue against language as an independent ability isolated from other cognitive abilities. We first review the evolution of global or "massive" modularity, as advocated by Fodor in his influential book (1983), to reduced local modularity, (Fodor, 2003). We then consider experimental data relevant to these issues: the emerging picture favors the view that music abilities, as well as other cognitive abilities (attention, memory, executive functions) influence language processing. These influences are seen in behavior as well as in the complex brain networks that sustain behavior. In sum, evidence is accumulating supporting the idea that the language system is not independent from other cognitive abilities.