The recent developments in the research area have seen significant advancements in sampling techniques and their applications across various domains. Notably, there is a strong focus on dimensionality-independent methods and gradient-free approaches, which are proving to be highly efficient and applicable, particularly in Bayesian inverse problems. The field is also witnessing innovations in mathematical morphology, particularly in handling higher-dimensional data, such as color representations, through novel approximations that maintain essential properties like associativity. Additionally, there are notable strides in the discretization of derivatives, with new error bounds being established for the Caputo derivative in Hölder spaces. Efficient averaging and matrix samplers are being developed, achieving near-optimal complexity in randomness and sample requirements, with applications extending to randomness extractors and list-decodable codes. The sampling of non-smooth log densities, crucial in Bayesian inverse problems, is being addressed through novel Hadamard Langevin dynamics, offering exact resolution without the bias introduced by traditional proximal methods. Ergodicity and convergence properties of Langevin dynamics for non-smooth potentials are also being rigorously studied, with practical implications in imaging applications. Lastly, nonlinear assimilation is being advanced through score-based sequential Langevin sampling, which demonstrates robust performance in high-dimensional and nonlinear scenarios, including sparse or partial measurements, while effectively quantifying uncertainty.