The brain changes profoundly in structure and function during development and as a result of diseases such as the dementias, schizophrenia, multiple sclerosis, and tumor growth. Strategies to measure, map, and visualize these brain changes are of immense value in basic and clinical neuroscience. Algorithms that map brain change with sufficient spatial and temporal sensitivity can also assess drugs that aim to decelerate or arrest these changes. In neuroscience studies, these tools can reveal subtle brain changes in adolescence and old age and link these changes with measurable differences in brain function and cognition. Early detection of brain change in patients at risk for dementia; tumor recurrence; or relapsing-remitting conditions, such as multiple sclerosis, is also vital for optimizing therapy. We review a variety of mathematical and computational approaches to detect structural brain change with unprecedented sensitivity, both spatially and temporally. The resulting four-dimensional (4-D) maps of brain anatomy are warehoused in population-based brain atlases. Here, statistical tools compare brain changes across subjects and across populations, adjusting for complex differences in brain structure. Brain changes in an individual can be compared with a normative database comprised of subjects matched for age, gender, and other demographic factors. These dynamic brain maps offer key biological markers for understanding disease progression and testing therapeutic response. The early detection of disease-related brain changes is also critical for possible pre-emptive intervention before the ravages of disease have set in.