Computation and simulation are key parts of the scientific project and are also central to understanding emergence. After a general discussion of the role of simulations in science, the chapter turns to the theory of computation, Turing machines and the Church-Turing principle. Limits to the scope of simulation would imply limits to science. Absolute limits would arise if some things are non-computable. Thinking about practical limits leads us to quantum computers, quantum simulations and an estimation of the computational capacity of the universe. The physical version of the Church-Turing principle states that if we can build a universal quantum computer we can simulate every physical system.