Recent advances suggest that the response of RNA metabolism to stress has an important role in the pathophysiology of neurodegenerative diseases, particularly amyotrophic lateral sclerosis, frontotemporal dementias and Alzheimer disease. RNA-binding proteins (RBPs) control the utilization of mRNA during stress, in part through the formation of membraneless organelles termed stress granules (SGs). These structures form through a process of liquid-liquid phase separation. Multiple biochemical pathways regulate SG biology. The major signalling pathways regulating SG formation include the mammalian target of rapamycin (mTOR)-eukaryotic translation initiation factor 4F (eIF4F) and eIF2α pathways, whereas the pathways regulating SG dispersion and removal are mediated by valosin-containing protein and the autolysosomal cascade. Post-translational modifications of RBPs also strongly contribute to the regulation of SGs. Evidence indicates that SGs are supposed to be transient structures, but the chronic stresses associated with ageing lead to chronic, persistent SGs that appear to act as a nidus for the aggregation of disease-related proteins. We suggest a model describing how intrinsic vulnerabilities within the cellular RNA metabolism might lead to the pathological aggregation of RBPs when SGs become persistent. This process might accelerate the pathophysiology of many neurodegenerative diseases and myopathies, and it suggests new targets for disease intervention.