Given that original purpose of cognitive architectures was to lead to a unified theory of cognition, this chapter considers the possible contributions that cognitive architectures can make to embodied theories of cognition in particular. This is not a trivial question since the field remains very much divided about what embodied cognition actually means, and we will see some example positions in this chapter. It is then argued that a useful embodied cognitive architecture would be one that can demonstrate (a) what precisely the role of the body in cognition actually is, and (b) whether a body is constitutively needed at all for some (or all) cognitive processes. It is proposed that such questions can be investigated if the cognitive architecture is designed so that consequences of varying the precise embodiment on higher cognitive mechanisms can be explored. This is in contrast with, for example, those cognitive architectures in robotics that are designed for specific bodies first; or architectures in cognitive science that implement embodiment as an add-on to an existing framework (because then, that framework is by definition not constitutively shaped by the embodiment). The chapter concludes that the so-called semantic pointer architecture by Eliasmith and colleagues may be one framework that satisfies our desiderata and may be well-suited for studying theories of embodied cognition further.