We develop the view that the involvement of mirror neurons in embodied experience grounds brain structures that underlie language, but that many other brain regions are involved. We stress the cooperation between the dorsal and ventral streams in praxis and language. Both have perceptual and motor schemas but the perceptual schemas in the dorsal path are affordances linked to specific motor schemas for detailed motor control, whereas the ventral path supports planning and decision making. This frames the hypothesis that the mirror system for words evolved from the mirror system for actions to support words-as-phonological-actions, with semantics provided by the linkage to neural systems supporting perceptual and motor schemas. We stress the importance of computational models which can be linked to the parametric analysis of data and conceptual analysis of these models to support new patterns of understanding of the data. In the domain of praxis, we assess the FARS model of the canonical system for grasping, the MNS models for the mirror system for grasping, and the Augmented Competitive Queuing model that extends the control of action to the opportunistic scheduling of action sequences and also offers a new hypothesis on the role of mirror neurons in self action. Turning to language, we use Construction Grammar as our linguistic framework to get beyond single words to phrases and sentences, and initiate analysis of what brain functions must complement mirror systems to support this functionality. (Contains 6 figures.)