Our impressive abilities to process complex sound and structure may be most evident in language and music. In fact, there is growing evidence that structural processing in language and music draws on shared cognitive and neural resources. However, other work suggests linguistic and musical structure draw on largely separable processes based, for example, on dissociations in brain damaged individuals. I will discuss studies aimed at resolving these discrepancies, and argue that language/music relationships reflect (at least in part) shared reliance on domain general mechanisms of cognitive control.