Stress granules are mRNA-protein granules that form when translation initiation is limited, and they are related to pathological granules in various neurodegenerative diseases. Super-resolution microscopy reveals stable substructures, referred to as cores, within stress granules that can be purified. Proteomic analysis of stress granule cores reveals a dense network of protein-protein interactions and links between stress granules and human diseases and identifies ATP-dependent helicases and protein remodelers as conserved stress granule components. ATP is required for stress granule assembly and dynamics. Moreover, multiple ATP-driven machines affect stress granules differently, with the CCT complex inhibiting stress granule assembly, while the MCM and RVB complexes promote stress granule persistence. Our observations suggest that stress granules contain a stable core structure surrounded by a dynamic shell with assembly, disassembly, and transitions between the core and shell modulated by numerous protein and RNA remodeling complexes.