Background: This study explores how mild cognitive impairment (MCI) and Alzheimer's disease (AD) develop over time. New method: this study involves a new application of latent curve models (LCM) to examine the development trajectory of a healthy, MCI, and AD groups on a series of clinical and neural measures. Multiple-group latent curve models were used to compare the parameters of the trajectories across groups. Results: LCM results showed that a linear functional form of growth was adequate for all the clinical and neural measures. Positive and significant differences in initial levels were seen across groups on all of the clinical and neural measures. In all groups, the following measures increased slightly, or considerably, over time: Clinical Dementia Rating, Alzheimer's disease Cognitive Assessment, and Montreal Assessment Test for Dementia. In contrast, a slight or a greatly decreasing trajectory was observed on the following measures: Fluorodeoxyglucose, Mini-Mental State Exam, Rey Auditory Verbal Learning Test as well as Hippocampus, Fusiform and Entorhinal Cortex volume measures. However, a constant mean trajectory was seen on Cognition Self Report Memory and languages scores. Comparision with existing methods: there are no prior studies that applied LCM on large AD datasets. Conclusions: cognitive decline occurs in the cognitively normal (CN), MCI, and AD groups but at different rates. Further, some important cognitive, neural, and clinical variables that (a) best differentiate between CN, MCI, and AD as well as (b) differentially change over time in MCI and AD, which may explain disease progression.