Friction stir welding (FSW) is a manufacturing process that many industries have adopted to join metals in a solid state, resulting in unique properties. However, studying aspects like temperature distribution, stress distribution, and material flow experimentally is challenging due to severe plastic deformation in the weld zone. Therefore, numerical methods are utilized to investigate these parameters and gain a better understanding of the FSW process. Numerical models are employed to simulate material flow, temperature distribution, and stress state during welding. This allows for the identification of potential defect-prone zones. This paper presents a comprehensive review of research activities and advancements in numerical analysis techniques specifically designed for friction stir welding, with a focus on their applicability to component manufacturing. The paper begins by examining various types of numerical methods and modeling techniques used in FSW analysis, including finite element analysis, computational fluid dynamics, and other simulation approaches. The advantages and limitations of each method are discussed, providing insights into their suitability for FSW simulations. Furthermore, the paper delves into the crucial variables that play a significant role in the numerical modeling of the FSW process.