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Neurodegenerative disorders and type 2 diabetes are global epidemics compromising the quality of life of millions worldwide, with profound social and economic implications. Despite the significant differences in pathology - much of which are poorly understood - these diseases are commonly characterized by the presence of cross-β amyloid fibrils as well as the loss of neuronal or pancreatic β-cells. In this review, we document research progress on the molecular and mesoscopic self-assembly of amyloid-beta, alpha synuclein, human islet amyloid polypeptide and prions, the peptides and proteins associated with Alzheimer's, Parkinson's, type 2 diabetes and prion diseases. In addition, we discuss the toxicities of these amyloid proteins based on their self-assembly as well as their interactions with membranes, metal ions, small molecules and engineered nanoparticles. Through this presentation we show the remarkable similarities and differences in the structural transitions of the amyloid proteins through primary and secondary nucleation, the common evolution from disordered monomers to alpha-helices and then to β-sheets when the proteins encounter the cell membrane, and, the consensus (with a few exceptions) that off-pathway oligomers, rather than amyloid fibrils, are the toxic species regardless of the pathogenic protein sequence or physicochemical properties. In addition, we highlight the crucial role of molecular self-assembly in eliciting the biological and pathological consequences of the amyloid proteins within the context of their cellular environments and their spreading between cells and organs. Exploiting such structure-function-toxicity relationship may prove pivotal for the detection and mitigation of amyloid diseases.