Classifying and predicting Alzheimer's disease (AD) in individuals with memory disorders through clinical and psychometric assessment is challenging, especially in mild cognitive impairment (MCI) subjects. Quantitative structural magnetic resonance imaging acquisition methods in combination with computer-aided diagnosis are currently being used for the assessment of AD. These acquisitions methods include voxel-based morphometry, volumetric measurements in specific regions of interest (ROIs), cortical thickness measurements, shape analysis, and texture analysis. This review evaluates the aforementioned methods in the classification of cases into one of the following three groups: normal controls, MCI, and AD subjects. Furthermore, the performance of the methods is assessed on the prediction of conversion from MCI to AD. In parallel, it is also assessed which ROIs are preferred in both classification and prognosis through the different states of the disease. Structural changes in the early stages of the disease are more pronounced in the medial temporal lobe, especially in the entorhinal cortex, whereas with disease progression, both entorhinal cortex and hippocampus offer similar discriminative power. However, for the conversion from MCI subjects to AD, entorhinal cortex provides better predictive accuracies rather than other structures, such as the hippocampus.