The goal of this review of the theories of cellular ageing is first to distinguish the theories on the basis of logical criteria following the dichotomies genetic/environmental and deterministic/stochastic. The second purpose is to show, from such criteria, that these theories can be integrated in a more general concept, which is the concept of critical threshold of error accumulation, taking into account the protective role of defenses systems avoiding a quick increase in the level of intracellular errors.