The Fragile X syndrome (FXS) is the most frequent form of inherited mental retardation and also considered a monogenic cause of Autism Spectrum Disorder. FXS symptoms include neurodevelopmental delay, anxiety, hyperactivity, and autistic-like behavior. The disease is due to mutations or loss of the Fragile X Mental Retardation Protein (FMRP), an RNA-binding protein abundant in the brain and gonads, the two organs mainly affected in FXS patients. FMRP has multiple functions in RNA metabolism, including mRNA decay, dendritic targeting of mRNAs, and protein synthesis. In neurons lacking FMRP, a wide array of mRNAs encoding proteins involved in synaptic structure and function are altered. As a result of this complex dysregulation, in the absence of FMRP, spine morphology and functioning is impaired. Consistently, model organisms for the study of the syndrome recapitulate the phenotype observed in FXS patients, such as dendritic spine anomalies and defects in learning. Here, we review the fundamentals of genetic and clinical aspects of FXS, devoting a specific attention to ASD comorbidity and FXS-related diseases. We also review the current knowledge on FMRP functions through structural, molecular, and cellular findings. Finally, we discuss the neuroanatomical, electrophysiological, and behavioral defects caused by FMRP loss, as well as the current treatments able to partially revert some of the FXS abnormalities.