Abstract: Semiclassical spin dynamics provides a powerful framework for studying finite-temperature magnetic excitations beyond the harmonic approximation, naturally incorporating nonlinear dynamics and thermal fluctuations. In this talk, I will discuss how real-time spin trajectories can be used to calculate response functions beyond the conventional dynamical structure factor, focusing on thermal Hall transport and Raman circular dichroism. I will present a framework for calculating the thermal Hall conductivity from equilibrium energy-current correlations, highlighting the roles of classical statistics and nonlinear finite-temperature effects. I will then discuss how impurity-induced chiral interactions can give rise to additional Raman scattering channels. Finally, I will explore possible approaches to incorporating quantum statistics into semiclassical spin dynamics, aiming to improve dynamical response functions while preserving nonlinear real-time dynamics.