Modern pharmacotherapy of neurodegenerative diseases is predominantly symptomatic and does not allow vicious circles causing disease development to break. Protein misfolding is considered the most important pathogenetic factor of neurodegenerative diseases. Physiological mechanisms related to the function of chaperones, which contribute to the restoration of native conformation of functionally important proteins, evolved evolutionarily. These mechanisms can be considered promising for pharmacological regulation. Therefore, the aim of this review was to analyze the mechanisms of endoplasmic reticulum stress (ER stress) and unfolded protein response (UPR) in the pathogenesis of neurodegenerative diseases. Data on BiP and Sigma1R chaperones in clinical and experimental studies of Alzheimer’s disease, Parkinson’s disease, amyotrophic lateral sclerosis, and Huntington’s disease are presented. The possibility of neuroprotective effect dependent on Sigma1R ligand activation in these diseases is also demonstrated. The interaction between Sigma1R and BiP-associated signaling in the neuroprotection is discussed. The performed analysis suggests the feasibility of pharmacological regulation of chaperone function, possibility of ligand activation of Sigma1R in order to achieve a neuroprotective effect, and the need for further studies of the conjugation of cellular mechanisms controlled by Sigma1R and BiP chaperones.