The term "amyloids" refers to fibrillar protein aggregates with cross-β structure. They have been a subject of intense scrutiny since the middle of the previous century. First, this interest is due to association of amyloids with dozens of incurable human diseases called amyloidoses, which affect hundreds of millions of people. However, during the last decade the paradigm of amyloids as pathogens has changed due to an increase in understanding of their role as a specific variant of quaternary protein structure essential for the living cell. Thus, functional amyloids are found in all domains of the living world, and they fulfill a variety of roles ranging from biofilm formation in bacteria to long-term memory regulation in higher eukaryotes. Prions, which are proteins capable of existing under the same conditions in two or more conformations at least one of which having infective properties, also typically have amyloid features. There are weighty reasons to believe that the currently known amyloids are only a minority of their real number. This review provides a retrospective analysis of stages in the development of amyloid biology that during the last decade resulted, on one hand, in reinterpretation of the biological role of amyloids, and on the other hand, in the development of systems biology of amyloids, or amyloidomics.