Non-membrane-bound compartments such as mRNA processing bodies (PBs) and stress granules (SGs) play important roles in the regulation of gene expression following environmental stresses. We have systematically determined the protein and mRNA composition of PBs and SGs formed in response to a common stress condition imposed by glucose depletion. We find that high molecular weight (HMW) complexes exist prior to glucose depletion that may act as seeds for the further condensation of proteins forming mature PBs and SGs. Both before and after glucose depletion, these HMW complexes are enriched for proteins containing low complexity and RNA binding domains. The mRNA content of these HMW complexes is enriched for long, structured mRNAs that become more poorly translated following glucose depletion. Many proteins and mRNAs are shared between PBs and SGs, suggesting a complex pattern of functional protein and mRNA pools exist in different condensates. Even where the precise identity of mRNAs and proteins localizing to PBs and SGs is distinct, the mRNAs and proteins share common biophysical and chemical features that likely trigger their phase separation.