Regulation of RNA homeostasis or “RNAstasis” is a central step in eukaryotic gene expression. From transcription to decay, cellular messenger RNAs (mRNAs) associate with specific proteins in order to regulate their entire cycle, including mRNA localization, translation and degradation, among others. The best characterized of such RNA-protein complexes, today named membraneless organelles, are Stress Granules (SGs) and Processing Bodies (PBs) which are involved in RNA storage and RNA decay/storage, respectively. Given that SGs and PBs are generally associated with repression of gene expression, viruses have evolved different mechanisms to counteract their assembly or to use them in their favor to successfully replicate within the host environment. In this review we summarize the current knowledge about the viral regulation of SGs and PBs, which could be a potential novel target for the development of broad-spectrum antiviral therapies.