Saliva is a biofluid that can be considered as a “mirror” reflecting our body’s health status. Vibrational spectroscopy, Raman and infrared, can provide a detailed salivary fingerprint that can be used for disease biomarker discovery. We propose a systematic literature review based on the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) guidelines to evaluate the potential of vibrational spectroscopy to diagnose oral and general diseases using saliva as a biological specimen. Literature searches were recently conducted in May 2020 through MEDLINE-PubMed and Scopus databases, without date limitation. Finally, over a period of 10 years, 18 publications were included reporting on 10 diseases (three oral and seven general diseases), with very high diagnostic performance rates in terms of sensitivity, specificity, and accuracy. Thirteen articles were related to six different cancers of the following anatomical sites: mouth, nasopharynx, lung, esophagus, stomach, and breast. The other diseases investigated and included in this review were periodontitis, Sjögren’s syndrome, diabetes, and myocardial infarction. Moreover, most articles focused on Raman spectroscopy (n = 16/18) and more specifically surface-enhanced Raman spectroscopy (n = 12/18). Interestingly, vibrational spectroscopy appears promising as a rapid, label-free, and non-invasive diagnostic salivary biometric tool. Furthermore, it could be adapted to investigate subclinical diseases—even if developmental studies are required.