Cellular automata are dynamical systems where space, time, and variables are discrete. They are shown on two-dimensional examples to be capable of non-numerical simulations of physics. They are useful for faithful parallel processing of lattice models. At another level, they exhibit behaviours and illustrate concepts that are unmistakably physical, such as non-ergodicity and order parameters, frustration, relaxation to chaos through period doublings, a conspicuous arrow of time in reversible microscopic dynamics, causality and light-cone, and non-separability. In general, they constitute exactly computable models for complex phenomena and large-scale correlations that result from very simple short-range interactions. The author studies their space, time, and intrinsic symmetries and the corresponding conservation laws, with an emphasis on the conservation of information obeyed by reversible cellular automata. 60 references.