The aggregation of a polypeptide chain into amyloid fibrils and their accumulation and deposition into insoluble plaques and intracellular inclusions is the hallmark of several misfolding diseases known as amyloidoses. Alzheimer′s, Parkinson′s and Huntington’s diseases are some of the approximately 50 amyloid diseases described to date. The identification and characterization of the molecular species critical for amyloid formation and disease development have been the focus of intense scrutiny. Methods such as X-ray and electron diffraction, solid-state nuclear magnetic resonance spectroscopy (ssNMR) and cryo-electron microscopy (cryo-EM) have been extensively used and they have contributed to shed a new light onto the structure of amyloid, revealing a multiplicity of polymorphic structures that generally fit the cross-β amyloid motif. The development of rational therapeutic approaches against these debilitating and increasingly frequent misfolding diseases requires a thorough understanding of the molecular mechanisms underlying the amyloid cascade. Here, we review the current knowledge on amyloid fibril formation for several proteins and peptides from a kinetic and thermodynamic point of view, the structure of the molecular species involved in the amyloidogenic process, and the origin of their cytotoxicity.