The concreteness effect (CE), namely a better performance with concrete compared to abstract concepts, is a constant feature in healthy people, and it usually increases in persons with aphasia (PWA). However, a reversal of the CE has been reported in patients affected by the semantic variant of Primary Progressive Aphasia (svPPA), a neurodegenerative disease characterized by anterior temporal lobe (ATL) atrophy. The present scoping review aims at identifying the extent of evidence regarding the abstract/concrete contrast in Alzheimer’s disease (AD) and svPPA and associated brain atrophy. Five online databases were searched up to January 2023 to identify papers where both concrete and abstract concepts were investigated. Thirty-one papers were selected and showed that while in patients with AD, concrete words were better processes than abstract ones, in most svPPA patients, there was a reversal of the CE, with five studies correlating the size of this effect with ATL atrophy. Furthermore, the reversal of CE was associated with category-specific impairments (living things) and with a selective deficit of social words. Future work is needed to disentangle the role of specific portions of the ATL in concept representation.