Heat shock proteins (Hsps) represent the most evolutionarily ancient, conserved, and universal system for protecting cells and the whole body from various types of stress. Among Hsps, the group of proteins with a molecular weight of 70 kDa (Hsp70) plays a particularly important role. These proteins are molecular chaperones that restore the native conformation of partially denatured proteins after exposure to proteotoxic forms of stress and are critical for the folding and intracellular trafficking of de novo synthesized proteins under normal conditions. Hsp70s are expressed at high levels in the central nervous system (CNS) of various animals and protect neurons from various types of stress, including heat shock, hypoxia, and toxins. Numerous molecular and behavioral studies have indicated that Hsp70s expressed in the CNS are important for memory formation. These proteins contribute to the folding and transport of synaptic proteins, modulate signaling cascades associated with synaptic activation, and participate in mechanisms of neurotransmitter release. In addition, HSF1, a transcription factor that is activated under stress conditions and mediates Hsps transcription, is also involved in the transcription of genes encoding many synaptic proteins, whose levels are increased in neurons under stress and during memory formation. Thus, stress activates the molecular mechanisms of memory formation, thereby allowing animals to better remember and later avoid potentially dangerous stimuli. Finally, Hsp70 has significant protective potential in neurodegenerative diseases. Increasing the level of endogenous Hsp70 synthesis or injecting exogenous Hsp70 reduces neurodegeneration, stimulates neurogenesis, and restores memory in animal models of ischemia and Alzheimer’s disease. These findings allow us to consider recombinant Hsp70 and/or Hsp70 pharmacological inducers as potential drugs for use in the treatment of ischemic injury and neurodegenerative disorders.