Silencing of the fragile X mental retardation 1 (FMR1) gene and consequently lack of synthesis of FMR protein (FMRP) are associated with fragile X syndrome, which is one of the most prevalent inherited intellectual disabilities. FMRP is a multifunctional protein involved in many cellular functions in nearly all subcellular compartments under normal conditions and under conditions of cellular stress in both 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 is modulated by various post-translational modifications such as phosphorylation, ubiquitination, sumoylation, and methylation. This review summarizes 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.