Stress granules are mRNA-protein granules that form when translation initiation is limited and 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, 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.