In Friction stir welding (FSW), the rotating and translating non-consumable tool generates frictional heat and softens the workpiece, which forms a metallurgical connection. Here, tool geometry selection, environmental parameter control, and mathematical modelling play vital roles in influencing weld quality and efficiency by optimizing heat generation and material flow to attain desired weld characteristics and to enable prediction and optimization of FSW processes, respectively. Through a meticulous and comprehensive review of existing state-of-the-art literature, the present work aims to shed light on these crucial aspects and provide insightful conclusions and future research directions. The Scopus database, a trusted source, has been utilized to extract the most relevant literature, ensuring a comprehensive and up-to-date review. Based on this review, we conclude that an FSW welding assistant, akin to electrical or cold assistance, yields finer grain structures and enhanced physical properties. Mathematical models in the literature primarily address welding speed and feed, with several parameters remaining unexplored; also, the tilt angle tools facilitate welding of complex angles, while dissimilar weld joints offer heightened corrosion. This review sets the stage for further exploration, envisioning FSW applications in the aerospace, automotive, marine, and defence sectors.