Certain cellular proteins normally soluble in the living organism under certain conditions form aggregates with a specific cross-β sheet structure called amyloid. These intra- or extracellular insoluble aggregates (fibers or plaques) are hallmarks of many neurodegenerative pathologies including Alzheimer's disease (AD), Huntington's disease, Parkinson's disease, prion disease, and other progressive neurological diseases that develop in the aging human central nervous system. Amyloid diseases (amyloidoses) are widespread in the elderly human population, a rapidly expanding demographic in many global populations. Increasing age is the most significant risk factor for neurodegenerative diseases associated with amyloid plaques. To date, nearly three dozen different misfolded proteins targeting brain and other organs have been identified in amyloid diseases and AD, the most prevalent neurodegenerative amyloid disease affecting over 15 million people worldwide. Here we (i) highlight the latest data on mechanisms of amyloid formation and further discuss a hypothesis on the amyloid cascade as a primary mechanism of AD pathogenesis and (ii) review the evolutionary aspects of amyloidosis, which allow new insight on human-specific mechanisms of dementia development.