Amyloid diseases are characterized by the deposition of typically aggregated proteins/peptides in tissues, associated with degeneration and progressive functional impairment. Alzheimer's disease is one of the most studied neurodegenerative amyloid diseases and, in Western countries, a significant cause of dementia in the elderly. The so-called "Mediterranean diet" has been considered for long as the healthier dietary regimen, characterised by a great abundance in vegetables and fruits, extra virgin olive oil as the main source of fat, a moderate consumption of red wine and a reduced intake of proteins from red meat. Recent epidemiological studies support the efficacy of the Mediterranean diet not only against cardiovascular and cancer diseases (as previously demonstrated) but also against the cognitive decline associated with ageing, and several data are highlighting the role played by natural phenols, of which red wine and extra virgin olive oil are rich, in such context. In the meantime, studies conducted both in vivo and in vitro have started to reveal the great potential of the phenolic component of extra virgin olive oil (mainly oleuropein aglycone and oleocanthal) in counteracting amyloid aggregation and toxicity, with a particular emphasis on the pathways involved in the onset and progression of Alzheimer's disease: amyloid precursor protein processing, amyloid-beta (Aβ) peptide and tau aggregation, autophagy impairment, neuroinflammation. The aim of this review is to summarize the results of such research efforts, showing how the action of these phenols goes far beyond their renowned antioxidant activity and revealing their potential as multi-targeting agents against Alzheimer's disease.