This review summarizes empirical findings and theoretical concepts in cognitive aging and late-life dementia research, with emphases on (a) person-to-person heterogeneity in trajectories of cognitive change over time, (b) how trajectories of child cognitive development determine peak levels of adult cognitive function from which aging-related cognitive declines occur, and (c) how lifelong trajectories of cognitive function relate to the timing of severe cognitive impairments characteristic of dementia. I consider conceptual issues surrounding categorical versus dimensional models of late-life dementia and discuss how current diagnostic approaches affect inferences in the empirical study of disease progression. Together, the incomplete current understanding of the biological foundations of aging-related cognitive declines and the continuous nature of many biomarkers commonly used in dementia diagnosis and classification pose both opportunities and challenges in the current research landscape. Future research will benefit from accurately measuring and analyzing continuous variation in longitudinal trajectories of cognitive function.