Stroke patients are more likely to develop dementia than age- and sex-matched controls but the pathogenesis of dementia remains unresolved in most of them. The aim of this review is to determine, from the available literature, the theoretical reasons for a stroke patient to become demented. We found three distinct factors that may explain the occurrence of dementia after a stroke. Firstly, post-stroke dementia may be the direct consequence of the vascular lesions of the brain: this is the most likely cause in patients with normal cognitive functions before a strategic infarct, especially in young patients, in Icelandic-type hereditary amyloid angiopathy and in cerebral autosomal dominant arteriopathy with subcortical infarcts and leucoencephalopathy. Secondly, post-stroke dementia may be due to an associated asymptomatic Alzheimer pathology; the reasons for such an association are that (1) some cases of dementia occurring after a stroke are progressive and Alzheimer's disease (AD) is the most frequent cause of progressive dementia; (2) age and APOE epsilon 4 genotype are risk factors for both AD and ischaemic stroke; (3) a vasculopathy is often associated with AD. Lastly, white matter changes may also contribute to dementia because they often indicate small-vessel disease and a higher risk of stroke recurrence, and may lead to slight cognitive impairment. Finally, the summation of vascular lesions of the brain, white matter changes, and Alzheimer pathology might lead to dementia, even when each type of lesion, on its own, is not severe enough to induce dementia. Therefore, in patients followed up after a stroke, the term "post-stroke dementia" is probably more appropriate than that of vascular dementia because it includes all possible causal factors.