Since the original description of amyloid-β plaques and tau tangles more than 100years ago, these lesions have been considered the neuropathological hallmarks of Alzheimer disease (AD). The prevalence of plaques, tangles and dementia increases with age, and the lesions are considered to be causally related to the cognitive symptoms of AD. Current schemes for assessing AD lesion burden examine the distribution, abundance and characteristics of plaques and tangles at post mortem, yielding an estimate of the likelihood of cognitive impairment. Although this approach is highly predictive for most individuals, in some instances, a striking mismatch between lesions and symptoms can be observed. A small subset of individuals harbour a high burden of plaques and tangles at autopsy, which would be expected to have had devastating clinical consequences, but remain at their cognitive baseline, indicating 'resilience'. The study of these brains might provide the key to understanding the 'black box' between the accumulation of plaques and tangles and cognitive impairment, and show the way towards disease-modifying treatments for AD. In this Review, we begin by considering the heterogeneity of clinical manifestations associated with the presence of plaques and tangles, and then focus on insights derived from the rare yet informative individuals who display high amounts of amyloid and tau deposition in their brains (observed directly at autopsy) without manifesting dementia during life. The resilient response of these individuals to the gradual accumulation of plaques and tangles has potential implications for assessing an individual's risk of AD and for the development of interventions aimed at preserving cognition.