Stress granules (SGs) are dynamic, reversible biomolecular condensates, which assemble in the cytoplasm of eukaryotic cells under various stress conditions. Formation of SGs typically occurs upon stress-induced translational arrest and polysome disassembly. The increase in cytoplasmic mRNAs triggers the formation of a protein-RNA network that undergoes liquid-liquid phase separation when a critical interaction threshold has been reached. This adaptive stress response allows a transient shutdown of several cellular processes until the stress is removed. During the recovery from stress, SGs disassemble to re-establish cellular activities. Persistent stress and disease-related mutations in SG components favor the formation of aberrant SGs that are impaired in disassembly and prone to aggregation. Recently, posttranslational modifications of SG components have been identified as major regulators of SG dynamics. Here, we summarize new insights into the role of ubiquitination in affecting SG dynamics and clearance and discuss implications for neurodegenerative diseases linked to aberrant SG formation.