Neurocognitive research is pertinent to developing mechanistic models of how humans generate creative thoughts. Such models usually overlook the role of the motor cortex in creative thinking. The framework of embodied or grounded cognition suggests that creative thoughts (e.g. using a shoe as a hammer, improvising a piano solo) are partially served by simulations of motor activity associated with tools and their use. The major hypothesis stemming from the embodied or grounded account is that, while the motor system is used to execute actions, simulations within this system also support higher-order cognition, creativity included. That is, the cognitive process of generating creative output, not just executing it, is deeply embedded in motor processes. Here, we highlight a collection of neuroimaging research that implicates the motor system in generating creative thoughts, including some evidence for its functionally necessary role in generating creative output. Specifically, the grounded or embodied framework suggests that generating creative output may, in part, rely on motor simulations of possible actions, and that these simulations may by partially implemented in the motor regions themselves. In such cases, action simulations (i.e. reactivating or re-using the motor system), do not result in overt action but instead are used to support higher-order cognitive goals like generating creative uses or improvising.