Human ageing is the gradual decline in organ and tissue function with increasing chronological time, leading eventually to loss of function and death. To study the processes involved over research-relevant timescales requires the use of accessible model systems that share significant similarities with humans. In this review, we assess the usefulness of various models, including unicellular yeasts, invertebrate worms and flies, mice and primates including humans, and highlight the benefits and possible drawbacks of each model system in its ability to illuminate human ageing mechanisms. We describe the strong evolutionary conservation of molecular pathways that govern cell responses to extracellular and intracellular signals and which are strongly implicated in ageing. Such pathways centre around insulin-like growth factor signalling and integration of stress and nutritional signals through mTOR kinase. The process of cellular senescence is evaluated as a possible underlying cause for many of the frailties and diseases of human ageing. Also considered is ageing arising from systemic changes that cannot be modelled in lower organisms and instead require studies either in small mammals or in primates. We also touch briefly on novel therapeutic options arising from a better understanding of the biology of ageing.