Recommended guidelines for the diagnosis of dementia due to Alzheimer's Disease (AD) were revised in recent years, including Positron Emission Tomography (PET) as an in-vivo diagnostic imaging technique for the diagnosis of neurodegeneration. In particular PET, using 18Ffluorodeoxiglucouse ([18F]FDG), is able to detect very early changes of glucose consumption at the synaptic level, enabling to support both early and differential diagnosis of AD. In standard clinical practice, interpretation of [18F] FDG-PET images is usually achieved through qualitative assessment. Visual inspection although only reveals information visible at human eyes resolution, while information at a higher resolution is missed. Furthermore, qualitative assessment depends on the degree of expertise of the clinician, preventing from the definition of accurate and standardized imaging biomarkers. Automated and computerized image processing methods have been proposed to support the in-vivo assessment of brain PET studies. In particular, objective statistical image analyses, enabling the comparison of one patient's images to a group of control images have been shown to carry important advantages for detecting significant metabolic changes, including the availability of more objective, cross-center reliable metrics and the detectability of brain subtle functional changes, as occurring in prodromal AD. The purpose of the current review is to provide a systematic overview encompassing the frontiers recently reached by quantitative approaches for the statistical analysis of PET brain images in the study of AD, with a particular focus on Statistical Parametric Mapping. Main achievements, e.g. in terms of standardized biomarkers of AD as well as of sensitivity and specificity, will be discussed.