The emergence of Alzheimer's Disease (AD) as a consequence of increasing aging population makes urgent the availability of methods for the early and accurate diagnosis. Magnetic Resonance Imaging (MRI) could be used as in vivo, non invasive tool to identify sensitive and specific markers of very early AD progression. In recent years, multivariate pattern analysis (MVPA) and machine- learning algorithms have attracted strong interest within the neuroimaging community, as they allow automatic classification of imaging data with higher performance than univariate statistical analysis. An exhaustive search of PubMed, Web of Science and Medline records was performed in this work, in order to retrieve studies focused on the potential role of MRI in aiding the clinician in early diagnosis of AD by using Support Vector Machines (SVMs) as MVPA automated classification method. A total of 30 studies emerged, published from 2008 to date. This review aims to give a state-of-the-art overview about SVM for the early and differential diagnosis of AD-related pathologies by means of MRI data, starting from preliminary steps such as image pre-processing, feature extraction and feature selection, and ending with classification, validation strategies and extraction of MRI-related biomarkers. The main advantages and drawbacks of the different techniques were explored. Results obtained by the reviewed studies were reported in terms of classification performance and biomarker outcomes, in order to shed light on the parameters that accompany normal and pathological aging. Unresolved issues and possible future directions were finally pointed out.