Employing numerical methods to simulate manufacturing processes and study their influential factors is increasing. The development of computers and engineering software has increased the ability and accuracy of numerical methods in simulating various aspects of different processes. One of the manufacturing processes that has been considered by many industries in recent years to join metals in solid-state with unique properties is called friction stir welding. It is challenging and, in some cases, impossible to experimentally study the various aspects of this process, such as temperature distribution, stress distribution, and material flow, due to severe plastic deformation in the weld zone. In this case, numerical methods are used to investigate these parameters and better understand the process. This study first investigates various numerical methods researchers use to simulate the process. The ability, pros, and cons of these methods to simulate the process are also examined. Then, the applications of numerical models in simulating the temperature distribution during the process as well as the effects of input parameters on the temperature history of the process, are deeply considered. Next, the application of numerical methods in material flow modeling during the process is investigated. Finally, the modeling of the microstructure of the welding zone is investigated using numerical methods that help significantly in predicting the weld microstructure.