Primary progressive aphasia (PPA) is caused by selective neurodegeneration of the language-dominant cerebral hemisphere; a language deficit initially arises as the only consequential impairment and remains predominant throughout most of the course of the disease. Agrammatic, logopenic and semantic subtypes, each reflecting a characteristic pattern of language impairment and corresponding anatomical distribution of cortical atrophy, represent the most frequent presentations of PPA. Such associations between clinical features and the sites of atrophy have provided new insights into the neurology of fluency, grammar, word retrieval, and word comprehension, and have necessitated modification of concepts related to the functions of the anterior temporal lobe and Wernicke's area. The underlying neuropathology of PPA is, most commonly, frontotemporal lobar degeneration in the agrammatic and semantic forms, and Alzheimer disease (AD) pathology in the logopenic form; the AD pathology often displays atypical and asymmetrical anatomical features consistent with the aphasic phenotype. The PPA syndrome reflects complex interactions between disease-specific neuropathological features and patient-specific vulnerability. A better understanding of these interactions might help us to elucidate the biology of the language network and the principles of selective vulnerability in neurodegenerative diseases. We review these aspects of PPA, focusing on advances in our understanding of the clinical features and neuropathology of PPA and what they have taught us about the neural substrates of the language network.