There currently exist a large number of interesting and intriguing empirical effects regarding embodied cognition. A critical next step in the development of embodied theories is to flesh out ideas in terms of implemented computational models. This symposium features speakers who currently are working toward that goal, including Giovanni Pezzulo, Angelo Cangelosi, and Michael Spivey, as well as discussion by Lawrence Barsalou, Martin Fischer, and Ken McRae. These researchers describe and discuss challenges for embodied models. The major focus is on presenting current efforts to model human cognition in a physical agent with sensory and motor capabilities, implementing the perceptual symbols systems framework, and modelling the dynamic on-line influences of integrated sensorimotor processes.