Cognitive theories of metaphor understanding are typically described in terms of the mappings between different kinds of abstract, schematic, disembodied knowledge. My claim in this paper is that part of our ability to make sense of metaphorical language, both individual utterances and extended narratives, resides in the automatic construction of a simulation whereby we imagine performing the bodily actions referred to in the language. Thus, understanding metaphorical expressions like 'grasp a concept' or 'get over' an emotion involve simulating what it must be like to engage in these specific activities, even though these actions are, strictly speaking, impossible to physically perform. This process of building a simulation, one that is fundamentally embodied in being constrained by past and present bodily experiences, has specific consequences for how verbal metaphors are understood, and how cognitive scientists, more generally, characterize the nature of metaphorical language and thought.