Viruses initiate a number of cellular stress responses and modulate gene regulation and compartmentalization of RNA upon infection to be successful parasites. Virus infections may induce or impair stress granule (SG) formation to maximize replication efficiency. SGs and processing bodies (PBs) are the RNA granules, which contain translationally inactive pool of transcripts as the mRNA silencing foci. PBs and SGs, the highly conserved macromolecular aggregates, can release mRNAs to allow their translations. Unlike constitutively existing PBs that can respond to stimuli and affect mRNA translation and decay, SGs are specifically induced upon cellular stress and can triggers a global translational silencing by several pathways, including phosphorylation of the key translation initiation factor eIF2alpha, tRNA cleavage, and sequestration of cellular components and so on. The dynamics of PBs and SGs are regulated by several signaling pathways, including histone deacetylase 6, and depend on microfilaments and microtubules, and the cognate molecular motors myosin, dynein, and kinesin. SGs share features with aggresomes and related aggregates of unfolded proteins and may play a role in the pathology. The recent advances in understanding the relationship between viruses and mRNA stress granules are summarized.