Dynamical low-rank (DLR) approximation has emerged as a powerful tool for on-the-fly model order reduction in solving high-dimensional PDEs, with significant recent advances in kinetic simulations. However, a major challenge with kinetic equations is that they often involve nonlinear operators and exhibit multiple scales, rendering a direct application of the DLR method inefficient. In this talk, I will use the nonlinear Boltzmann equation, a fundamental equation in kinetic theory, to demonstrate how one can achieve efficient DLR approximation for such problems, while preserving key structural properties of the solution.