Abstract: Radiative transfer equations (RTEs) are fundamental models to describe the physical phenomena of energy or particle transport through mediums that are affected by absorption, emission, and scattering processes. Deterministic simulations can provide an accurate description of the solutions; they however face many computational challenges, most prominently the need to compute the angular flux defined in the high dimensional phase space. In this talk, we will share our work in developing reduced basis methods (RBMs) for the stationary RTE. In the single-query setting, our RBM is designed by leveraging the low-rank structure of the angle-induced solution manifold in or near the scattering dominant regime. In the multi-query setting, four RBM-based ROMs are formulated for the parametric RTE, with one major technical focus on implementation strategies, to ensure ultimate efficiency and robustness of the entire model reduction algorithm under the affine assumption of the parameter dependence. The work is in collaboration with Y. Chen (UMass Dartmouth), Y. Cheng (Virginia Tech), Kimberly Matsuda (Rensselaer Polytechnic Institute) and Z. Peng (Hong Kong Univ. of Science and Technology).