Amyloids represent protein fibrils that have highly ordered structure with unique physical and chemical properties. Amyloids have long been considered lethal pathogens that cause dozens of incurable diseases in humans and animals. Recent data show that amyloids may not only possess pathogenic properties but are also implicated in the essential biological processes in a variety of prokaryotes and eukaryotes. Functional amyloids have been identified in archaea, bacteria, fungi, and animals, including humans. Plants are one of the most poorly studied groups of organisms in the field of amyloid biology. Although amyloid properties have not been shown under native conditions for any plant protein, studies demonstrating amyloid properties for a set of plant proteins in vitro or in heterologous systems in vivo have been published in recent years. In this review, we systematize the data on the amyloidogenic proteins of plants and their functions and discuss the perspectives of identifying novel amyloids using bioinformatic and proteomic approaches.