In cells at steady state, two forms of cell compartmentalization coexist: membrane-bound organelles and phase-separated membraneless organelles that are present in both the nucleus and the cytoplasm. Strikingly, cellular stress is a strong inducer of the reversible membraneless compartments referred to as stress assemblies. Stress assemblies play key roles in survival during cell stress and in thriving of cells upon stress relief. The two best studied stress assemblies are the RNA-based processing-bodies (P-bodies) and stress granules that form in response to oxidative, endoplasmic reticulum (ER), osmotic and nutrient stress as well as many others. Interestingly, P-bodies and stress granules are heterogeneous with respect to both the pathways that lead to their formation and their protein and RNA content. Furthermore, in yeast and Drosophila, nutrient stress also leads to the formation of many other types of prosurvival cytoplasmic stress assemblies, such as metabolic enzymes foci, proteasome storage granules, EIF2B bodies, U-bodies and Sec bodies, some of which are not RNA-based. Nutrient stress leads to a drop in cytoplasmic pH, which combined with posttranslational modifications of granule contents, induces phase separation.