Silencing of the fragile X messenger ribonucleoprotein 1 (FMR1) gene and a consequent lack of FMR protein (FMRP) synthesis are associated with fragile X syndrome, one of the most common inherited intellectual disabilities. FMRP is a multifunctional protein that is involved in many cellular functions in almost all subcellular compartments under both normal and cellular stress conditions in neuronal and non-neuronal cell types. This is achieved through its trafficking signals, nuclear localization signal (NLS), nuclear export signal (NES), and nucleolar localization signal (NoLS), as well as its RNA and protein binding domains, and it is modulated by various post-translational modifications such as phosphorylation, ubiquitination, sumoylation, and methylation. This review summarizes the recent advances in understanding the interaction networks of FMRP with a special focus on FMRP stress-related functions, including stress granule formation, mitochondrion and endoplasmic reticulum plasticity, ribosome biogenesis, cell cycle control, and DNA damage response.