The field of stochastic numerical analysis is witnessing significant developments, with a focus on improving the accuracy and efficiency of numerical methods for solving stochastic differential equations. Researchers are exploring new approaches, such as resonance-based integrators and intrinsic methods on Riemannian manifolds, to tackle challenging problems in stochastic dynamics. These innovative methods are enabling the solution of complex equations with lower regularity solutions, and are achieving provable convergence and improved strong convergence rates. Notably, the use of space-time bounds and null form estimates is leading to optimal convergence rates for certain integrators. Some noteworthy papers in this area include: A Wong--Zakai resonance-based integrator for nonlinear Schrödinger equation with white noise dispersion, which introduces a novel approach to numerical approximation of nonlinear Schrödinger equation with white noise dispersion. High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods, which presents a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds.