Dementia remains an underdiagnosed syndrome, and there is a need to improve the early detection of cognitive decline. This narrative review examines the role of neuropsychological assessment in the characterization of cognitive changes associated with dementia syndrome at different states. The first section describes the early indicators of cognitive decline and the major barriers to their identification. Further, the optimal cognitive screening conditions and the most widely accepted tests are described. The second section analyzes the main differences in cognitive performance between Alzheimer’s disease and other subtypes of dementia. Finally, the current challenges of neuropsychological assessment in aging/dementia and future approaches are discussed. Essentially, we find that current research is beginning to uncover early cognitive changes that precede dementia, while continuing to improve and refine the differential diagnosis of neurodegenerative disorders that cause dementia. However, neuropsychology faces several barriers, including the cultural diversity of the populations, a limited implementation in public health systems, and the adaptation to technological advances. Nowadays, neuropsychological assessment plays a fundamental role in characterizing cognitive decline in the different stages of dementia, but more efforts are needed to develop harmonized procedures that facilitate its use in different clinical contexts and research protocols.