<p>Radiation belt dynamics remain a central problem in space physics, with direct implications for space weather prediction. Physical modeling of radiation belts is most often based on quasilinear theory, which assumes broadband, incoherent waves and treats particle transport as stochastic diffusion, leading to a Fokker–Planck–type diffusion equation for phase–space evolution. This framework, however, faces two major challenges: the breakdown of quasilinear assumptions under coherent wave conditions, and the numerical solution of multi–dimensional diffusion equations. This review summarizes recent progress on both fronts. The first concerns quasi–coherent interactions between electrons and chorus waves, long debated as either coherent nonlinear processes or stochastic diffusion. Recent theoretical and numerical studies indicate that such interactions are coherent on short timescales but effectively diffusive on longer ones, and we discuss how these effects can be incorporated into the diffusion framework. The second concerns numerical modeling: even with accurate diffusion coefficients, standard methods may yield unphysical negative phase–space densities. We review recent advances, including stochastic differential equation methods and positivity–preserving finite volume schemes, that overcome this difficulty. Together, these developments highlight how progress in both physical understanding and numerical methodology is essential for constructing predictive and physically consistent radiation belt models.</p>