Touch-screen tablet computers are emerging as a popular platform for many applications, including those in learning and model demonstration and parameter exploration. The human-computer interaction (HCI) mechanisms and potential of such devices make them attractive for highly interactive simulations. We have implemented a number of simulation models including: the Ising model of magnetism; di↵usion models; Conway's Game of Life and variants of it; and other cellular automata models. We show how the touch screen capability leads to new ways for users to interact with a running simulation-to steer the computations and to explore parameter model space. We describe our HCI and user-interface experiments and experiences on various Android Apps and discuss possible future directions for interfacing to such highly interactive models on tablet computers using native App programs as well as using web platform approaches.