The stochastic finite element method (SFEM) is a powerful tool in computational stochastic mechanics, extending the classical deterministic finite element method to handle problems with stochastic properties. The article provides a comprehensive review of past and recent developments in SFEM, highlighting its significance due to advancements in computational power that enable efficient treatment of large-scale problems. The first half of the article focuses on methods for simulating stochastic processes and fields, including Gaussian and non-Gaussian approaches. The second half delves into the variants of SFEM, such as the perturbation approach, spectral stochastic finite element method (SSFEM), and Monte Carlo simulation (MCS). It discusses the discretization of stochastic fields, the formulation of the stochastic matrix, and the calculation of response statistics. The article also addresses the choice of the "stochastic mesh" and its relationship with the finite element mesh, emphasizing the importance of selecting appropriate discretization methods and mesh sizes to ensure accurate and efficient solutions. Finally, it outlines future directions and open issues in the field, aiming to guide further research and application in computational stochastic mechanics.The stochastic finite element method (SFEM) is a powerful tool in computational stochastic mechanics, extending the classical deterministic finite element method to handle problems with stochastic properties. The article provides a comprehensive review of past and recent developments in SFEM, highlighting its significance due to advancements in computational power that enable efficient treatment of large-scale problems. The first half of the article focuses on methods for simulating stochastic processes and fields, including Gaussian and non-Gaussian approaches. The second half delves into the variants of SFEM, such as the perturbation approach, spectral stochastic finite element method (SSFEM), and Monte Carlo simulation (MCS). It discusses the discretization of stochastic fields, the formulation of the stochastic matrix, and the calculation of response statistics. The article also addresses the choice of the "stochastic mesh" and its relationship with the finite element mesh, emphasizing the importance of selecting appropriate discretization methods and mesh sizes to ensure accurate and efficient solutions. Finally, it outlines future directions and open issues in the field, aiming to guide further research and application in computational stochastic mechanics.