Friction stir welding (FSW) is a pivotal technology with ongoing relevance across industries. Renowned for its ability to join materials with dissimilar melting points while mitigating thermal distortions, FSW offers relevant advantages over traditional fusion welding. However, the adoption of FSW for high-strength alloys poses notable challenges, including: (i) accelerated tool wear, (ii) the need for special tool features tailored to these alloys, and (iii) a narrow process window. This review provides a comprehensive overview of FSW as an advanced technique for joining metal alloys for several industrial fields. Emphasis is on materials such as Mg-, Cu-, Ti-, and Ni-based alloys, automotive steels, stainless steels, and maraging steels. The research highlights the critical influence of tool design—main dimensions, features, and materials—and process parameters—rotational and welding speeds, tilt angle, and plunge depth or vertical load—also considering their influences on defect formation. Detailed insights are provided into material flow and the formation of the different weld regions, including SZ, TMAZ, and HAZ.