Alzheimer's disease (AD) is the most common neurodegenerative disorder for those 65 years or older; it currently affects 4.5 million in the United States and is predicted to rise to 13.2 million by the year 2050. Neuroimaging and brain mapping techniques offer extraordinary power to understand AD, providing spatially detailed information on the extent and trajectory of the disease as it spreads in the living brain. Computational anatomy techniques, applied to large databases of brain MRI scans, reveal the dynamic sequence of cortical and hippocampal changes with disease progression and how these relate to cognitive decline and future clinical outcomes. People who are mildly cognitively impaired, in particular, are at a fivefold increased risk of imminent conversion to dementia, and they show specific structural brain changes that are predictive of imminent disease onset. We review the principles and key findings of several new methods for assessing brain degeneration, including voxel-based morphometry, tensor-based morphometry, cortical thickness mapping, hippocampal atrophy mapping, and automated methods for mapping ventricular anatomy. Applications to AD and other dementias are discussed, with a brief review of related findings in other neurological and neuropsychiatric illnesses, including epilepsy, HIV/AIDS, schizophrenia, and disorders of brain development.