Geographical origin assessment of extra virgin olive oil (EVOO) is recognised worldwide as raising consumers' awareness of product authenticity and the need to protect top-quality products. The need for geographical origin assessment is also related to mandatory legislation and/or the obligations of true labelling in some countries. Nevertheless, official methods for such specific authentication of EVOOs are still missing. Among the analytical techniques useful for certification of geographical origin, nuclear magnetic resonance (NMR) and mass spectroscopy (MS), combined with chemometrics, have been widely used. This review considers published works describing the use of these analytical methods, supported by statistical protocols such as multivariate analysis (MVA), for EVOO origin assessment. The research has shown that some specific countries, generally corresponding to the main worldwide producers, are more interested than others in origin assessment and certification. Some specific producers such as Italian EVOO producers may have been focused on this area because of consumers' interest and/or intrinsic economical value, as testified also by the national concern on the topic. Both NMR- and MS-based approaches represent a mature field where a general validation method for EVOOs geographic origin assessment could be established as a reference recognised procedure.