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The prevalence of neurodegenerative disorders is increasing, partly owing to extensions in lifespan, but effective treatments are still lacking. This Insight explores brain ageing and possible rejuvenation and updates our understanding of Alzheimer’s disease, amyotrophic lateral sclerosis and Parkinson’s disease. It also reveals how knowledge from prion disease may apply to more common neurodegenerative disorders and provides a structural perspective on the properties of amyloids.