The logopenic variant of primary progressive aphasia is characterized by early deficits in language production and phonological short-term memory, attributed to left-lateralized temporoparietal, inferior parietal and posterior temporal neurodegeneration. Despite patients primarily complaining of language difficulties, emerging evidence points to performance deficits in non-linguistic domains. Temporoparietal cortex, and functional brain networks anchored to this region, are implicated as putative neural substrates of non-linguistic cognitive deficits in logopenic variant primary progressive aphasia, suggesting that degeneration of a shared set of brain regions may result in co-occurring linguistic and non-linguistic dysfunction early in the disease course. Here, we provide a Review aimed at broadening the understanding of logopenic variant primary progressive aphasia beyond the lens of an exclusive language disorder. By considering behavioural and neuroimaging research on non-linguistic dysfunction in logopenic variant primary progressive aphasia, we propose that a significant portion of multidimensional cognitive features can be explained by degeneration of temporal/inferior parietal cortices and connected regions. Drawing on insights from normative cognitive neuroscience, we propose that these regions underpin a combination of domain-general and domain-selective cognitive processes, whose disruption results in multifaceted cognitive deficits including aphasia. This account explains the common emergence of linguistic and non-linguistic cognitive difficulties in logopenic variant primary progressive aphasia, and predicts phenotypic diversification associated with progression of pathology in posterior neocortex.