Amyloids are unbranched protein fibrils with a characteristic spatial structure. Although the amyloids were first described as protein deposits that are associated with the diseases, today it is becoming clear that these protein fibrils play multiple biological roles that are essential for different organisms, from archaea and bacteria to humans. The appearance of amyloid, first of all, causes changes in the intracellular quantity of the corresponding soluble protein(s), and at the same time the aggregate can include other proteins due to different molecular mechanisms. The co-aggregation may have different consequences even though usually this process leads to the depletion of a functional protein that may be associated with different diseases. The protein co-aggregation that is related to functional amyloids may mediate important biological processes and change of protein functions. In this review, we survey the known examples of the amyloid-related co-aggregation of proteins, discuss their pathogenic and functional roles, and analyze methods of their studies from bacteria and yeast to mammals. Such analysis allow for us to propose the following co-aggregation classes: (i) titration: deposition of soluble proteins on the amyloids formed by their functional partners, with such interactions mediated by a specific binding site; (ii) sequestration: interaction of amyloids with certain proteins lacking a specific binding site; (iii) axial co-aggregation of different proteins within the same amyloid fibril; and, (iv) lateral co-aggregation of amyloid fibrils, each formed by different proteins.