Cellular stress has been considered a relevant pathogenetic factor in a variety of human diseases. Due to its primary functions by means of contractility, metabolism, and protein synthesis, the muscle cell is faced with continuous changes of cellular homeostasis that require rapid and coordinated adaptive mechanisms. Hence, a prone susceptibility to cellular stress in muscle is immanent. However, studies focusing on the cellular stress response in muscular disorders are limited. While in recent years there have been emerging indications regarding a relevant role of cellular stress in the pathophysiology of several muscular disorders, the underlying mechanisms are to a great extent incompletely understood. This review aimed to summarize the available evidence regarding a deregulation of the cellular stress response in individual muscle diseases. Potential mechanisms, as well as involved pathways are critically discussed, and respective disease models are addressed. Furthermore, relevant therapeutic approaches that aim to abrogate defects of cellular stress response in muscular disorders are outlined.