This review considers the recent progress on the role of heat shock proteins (HSPs), as well as transcription factors of heat shock proteins genes (HSFs) in protecting plants from oxidative stress induced by various types of abiotic and biotic stresses. HSPs are pleiotropic proteins involved in various intracellular processes and performing many important functions. In particular, HSPs increase plant resistance to stress by protecting the structure and activity of proteins of the antioxidant system. Overexpression of Hsp genes under stressful conditions, leading to an increased content of HSPs, can be used as a marker of oxidative stress. Plant HSFs are encoded by large gene families with variable sequences, expression and function. Plant HSFs regulate transcription of a wide range of stress-induced genes, including HSPs and other chaperones, reactive oxygen species scavengers, enzymes involved in protective metabolic reactions and osmolytic biosynthesis, or other transcriptional factors. Genome-wide analysis of Arabidopsis, rice, poplar, lettuce, and wheat revealed a complex network of interaction between the Hsps and Hsfs gene families that form plant protection against oxidative stress. Plant protection systems are discussed, with special emphasis on the role of HSPs and HSFs in plant responses to stress, which will be useful for the development of technologies to increase productivity and stress resistance of plant crops.