Between the 1930s and 1960s, evolutionary geneticists worked out the basic principles of why organisms age. Despite much progress in the evolutionary biology of ageing since that time, however, many puzzles remain. The perhaps most fundamental of these is the question of which organisms should exhibit senescence and which should not (or which should age rapidly and which should not). The evolutionary origin of ageing from a non-senescent state has been conceptually framed, for example, in terms of the separation between germ-line and soma, the distinction between parents and their offspring, and-in unicellular organisms-the unequal distribution of cellular damage at cell division. These ideas seem to be closely related to the concept of 'division of labour' between reproduction and somatic maintenance. Here, we review these concepts and develop a toy model to explore the importance of such asymmetries for the evolution of senescence. We apply our model to the simplest case of a multicellular system: an organism consisting of two totipotent cells. Notably, we find that in organisms which reproduce symmetrically and partition damage equally, senescence is still able to evolve, contrary to previous claims. Our results might have some bearing on understanding the origin of the germ-line-soma separation and the evolution of senescence in multicellular organisms and in colonial species consisting of multiple types of individuals, such as, for example, eusocial insects with their different castes. This article is part of the theme issue 'Ageing and sociality: why, when and how does sociality change ageing patterns?'