This chapter is dedicated to computational universalities in cellular automata, essentially Turing universality, the ability to compute any recursive function, and intrinsic universality, the ability to simulate any other cellular automaton. Constructions of Boolean circuits simulation in the two-dimensional case are explained in detail to achieve both kinds of universality. A detailed chronology of seminal papers is given, followed by a brief discussion of the formalization of universalities. The more difficult one-dimensional case is then discussed. Seminal universal cellular automata and encoding techniques are presented in both dimensions.
