A longstanding debate in dementia research has been whether normal aging and Alzheimer’s disease (AD) are extremes that lie along the same continuum (continuity view), or whether AD is categorically different from normal aging (discontinuity view). In other words, do only quantitative differences in neuropsychological test performance exist between normal aging and AD, or are there also qualitative differences? This question has been dominating dementia research for a century now and is characterized by inconsistent results and differences in methodological approach. In this review, I discuss studies that draw conclusions in terms of a continuous transition from normal aging to AD, followed by a discussion of studies that draw conclusions in terms of a discontinuous transition. In addition, several methodological issues are discussed that may explain the contrasting findings. This led to a proposal for investigating this topic in further research. I argue that only a latent variable (structural equation modeling) approach testing for measurement equivalence may or may not reveal structural (i.e. qualitative) differences in neuropsychological test performance between normal aging and AD. This outcome has important implications for the selection of optimal procedures of early AD assessment, particularly at very old age.