Heat shock (HS) is one of the best-studied exogenous cellular stresses. The cellular response to HS utilizes ancient molecular networks that are based primarily on the action of stress-induced heat shock proteins and HS factors. However, in one way or another, all cellular compartments and metabolic processes are involved in such a response. In this review, we aimed to summarize the experimental data concerning all aspects of the HS response in mammalian cells, such as HS-induced structural and functional alterations of cell membranes, the cytoskeleton and cellular organelles; the associated pathways that result in different modes of cell death and cell cycle arrest; and the effects of HS on transcription, splicing, translation, DNA repair, and replication.