Amyloid and amyloid-like aggregates are elongated unbranched fibrils consisting of β-structures of separate monomers positioned perpendicular to the fibril axis and stacked strictly above each other. In their physicochemical properties, amyloid fibrils are reminiscent of synthetic polymers rather than usual proteins because they are stable to the action of denaturing agents and proteases. Their mechanical stability can be compared to a spider's web, that in spite of its ability to stretch, is stronger than steel. It is not surprising that a large number of diseases are accompanied with amyloid fibril depositing in different organs. Pathologies provoked by depositing of incorrectly folded proteins include Alzheimer's, Parkinson's, and Huntington's diseases. In addition, this group of diseases involves mucoviscidosis, some types of diabetes, and hereditary cataracts. Each type of amyloidosis is characterized by aggregation of a certain type of protein that is soluble in general, and thus leads to specific distortions of functions of the corresponding organs. Therefore, it is important to understand the process of transformation of "native" proteins to amyloid fibrils to clarify how these molecules acquire such strength and what key elements of this process determine the pathway of erroneous protein folding. This review presents our analysis of complied information on the mechanisms of formation and biochemical properties of amyloid fibrils.