Stress granules (SGs) are phase-separated, membraneless, cytoplasmic ribonucleoprotein (RNP) assemblies whose primary function is to promote cell survival by condensing translationally stalled mRNAs, ribosomal components, translation initiation factors, and RNA-binding proteins (RBPs). While the protein composition and the function of proteins in the compartmentalization and the dynamics of assembly and disassembly of SGs has been a matter of study for several years, the role of RNA in these structures had remained largely unknown. RNA species are, however, not passive members of RNA granules in that RNA by itself can form homo and heterotypic interactions with other RNA molecules leading to phase separation and nucleation of RNA granules. RNA can also function as molecular scaffolds recruiting multivalent RBPs and their interactors to form higher-order structures. With the development of SG purification techniques coupled to RNA-seq, the transcriptomic landscape of SGs is becoming increasingly understood, revealing the enormous potential of RNA to guide the assembly and disassembly of these transient organelles. SGs are not only formed under acute stress conditions but also in response to different diseases such as viral infections, cancer, and neurodegeneration. Importantly, these granules are increasingly being recognized as potential precursors of pathological aggregates in neurodegenerative diseases. In this review, we examine the current evidence in support of RNA playing a significant role in the formation of SGs and explore the concept of SGs as therapeutic targets.