Amyloid diseases are global epidemics with profound health, social and economic implications and yet remain without a cure. This dire situation calls for research into the origin and pathological manifestations of amyloidosis to stimulate continued development of new therapeutics. In basic science and engineering, the cross-β architecture has been a constant thread underlying the structural characteristics of pathological and functional amyloids, and realizing that amyloid structures can be both pathological and functional in nature has fuelled innovations in artificial amyloids, whose use today ranges from water purification to 3D printing. At the conclusion of a half century since Eanes and Glenner's seminal study of amyloids in humans, this review commemorates the occasion by documenting the major milestones in amyloid research to date, from the perspectives of structural biology, biophysics, medicine, microbiology, engineering and nanotechnology. We also discuss new challenges and opportunities to drive this interdisciplinary field moving forward.