Research on polymer crystallization induced by flow has been one of the most fascinating topics in the field of polymer science. Structural changes during polymer crystallization induced by flow follow a multiscale and multistep mechanism. However, the structural changes are complex and rapid, making it challenging to accurately observe them online in experiments. Fortunately, computer molecular simulations provide a solution by allowing us to obtain detailed information about the microstructures at different stages and scales. This enables the simulation results to provide more accurate and comprehensive explanations of the microscopic mechanisms of flow-induced crystallization. In this Review, we delve into flow-induced microstructural evolutions, including conformational transition, segmental orientation, precursor formation, and shish formation, based on the results of molecular simulations. We also discuss the mechanisms of polymer nucleation induced by flow, including the formation mechanism of precursors, nucleation mode, the respective functions of chains with different lengths, the effect of nanofillers, and the effect of entanglements. Finally, we outline the future directions for simulation work on flow-induced crystallization. This includes the need for further investigation of the effects of entanglements on local segment orientation and precursor formation as well as the development of models capable of simulating the crystallization of different polymer materials. We also anticipate that the methods related to artificial intelligence, such as machine learning or deep learning, will play a significant role in constructing complex nonlinear relationships between the crystalline structure and mechanical properties.