The Hamilton–Jacobi–Bellman (HJB) equation plays a central role in optimal control and differential games, as it enables the computation of robust feedback controls. However, its practical applicability is severely limited by the curse of dimensionality, since both the HJB equation and the underlying dynamical system are defined on the same, potentially high-dimensional, state space. In this talk, I will present a data-driven approach for approximating high-dimensional HJB equations based on tensor decompositions. The proposed method relies on sampled evaluations of the value function and on a tensor-train representation to obtain an efficient low-rank approximation. The required data are collected using different strategies, ranging from State-Dependent Riccati Equation techniques to iterative schemes such as Policy Iteration. Finally, I will present an extension of the proposed framework to Mean Field Games, highlighting how the tensor-based approach can be adapted to handle the additional coupling structure.