Neural overlap in processing music and speech, as measured by the co-activation of brain regions in neuroimaging studies, may suggest that parts of the neural circuitries established for language may have been recycled during evolution for musicality, or vice versa that musicality served as a springboard for language emergence. Such a perspective has important implications for several topics of general interest besides evolutionary origins. For instance, neural overlap is an important premise for the possibility of music training to influence language acquisition and literacy. However, neural overlap in processing music and speech does not entail sharing neural circuitries. Neural separability between music and speech may occur in overlapping brain regions. In this paper, we review the evidence and outline the issues faced in interpreting such neural data, and argue that converging evidence from several methodologies is needed before neural overlap is taken as evidence of sharing.