Stress-induced condensation of mRNA and protein into massive cytosolic clusters is conserved across eukaryotes. Known as stress granules when visible by imaging, these structures remarkably have no broadly accepted biological function, mechanism of formation or dispersal, or even molecular composition. As part of a larger surge of interest in biomolecular condensation, studies of stress granules and related RNA/protein condensates have increasingly probed the biochemical underpinnings of condensation. Here, we review open questions and recent advances, including the stages from initial condensate formation to accumulation in mature stress granules, mechanisms by which stress-induced condensates form and dissolve, and surprising twists in understanding the RNA components of stress granules and their role in condensation. We outline grand challenges in understanding stress-induced RNA condensation, centering on the unique and substantial barriers in the molecular study of cellular structures, such as stress granules, for which no biological function has been firmly established.