Language disorders of degenerative origin are frequently tied to Alzheimer disease (AD) the different variants of which can result in primary and secondary aphasia syndromes. More specifically, Alzheimer pathology can primarily erode frontal, temporal or parietal language cortices resulting in three genuine AD language variants which account for about 30% of primary degenerative aphasias. Likewise, it can spread from non-language to language cortices leading to secondary language disorders like in typical amnesic AD and in several atypical AD variants. This paper reviews the whole set of AD variants by characterising their impact on the neural language system and on linguistic functioning. It also provides cues for diagnostic strategies which are essential for linguistic, syndromic and nosological patient classification, for adequate clinical follow-up and for guiding language rehabilitation. Such diagnostic approaches, founded on detailed linguistic phenotyping while integrating anatomical and neuropathological findings, also represent a crucial issue for future drug trials targeting the physio-pathological processes in degenerative aphasias.