Mean field games (MFGs) provide a powerful framework for modeling decision-making in large populations of interacting agents. However, solving high-dimensional MFG problems remains a significant computational challenge due to the curse of dimensionality. In this talk, we present a novel approach based on combining Semi-Lagrangian (SL) schemes with tensor-train (TT) decompositions to efficiently approximate solutions of high-dimensional MFGs. Semi-Lagrangian (SL) schemes allow us to derive a semi discrete in time approximations of the Hamilton-Jacobi-Bellman and Fokker-Planck-Kolmogorov equations, inherent in MFG models. By combining TT representations with SL discretizations, we achieve a scalable and memory-efficient numerical scheme that mitigates the exponential growth in computational complexity. We discuss theoretical properties of the method, numerical accuracy, and demonstrate its effectiveness through computational experiments on high-dimensional test cases.