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Epigenetic changes are known to accrue in normal cells as a result of ageing and cumulative exposure to cancer risk factors. Increasing evidence points towards age-related epigenetic changes being acquired in a quasi-stochastic manner, and that they may play a causal role in cancer development. Here, I describe the quasi-stochastic nature of DNA methylation (DNAm) changes in ageing cells as well as in normal cells at risk of neoplastic transformation, discussing the implications of this stochasticity for developing cancer risk prediction strategies, and in particular, how it may require a conceptual paradigm shift in how we select cancer risk markers. I also describe the mounting evidence that a significant proportion of DNAm changes in ageing and cancer development are related to cell proliferation, reflecting tissue-turnover and the opportunity this offers for predicting cancer risk via the development of epigenetic mitotic-like clocks. Finally, I describe how age-associated DNAm changes may be causally implicated in cancer development via an irreversible suppression of tissue-specific transcription factors that increases epigenetic and transcriptomic entropy, promoting a more plastic yet aberrant cancer stem-cell state.This article is part of a discussion meeting issue 'Causes and consequences of stochastic processes in development and disease'.