The field of dynamical systems is witnessing significant developments in spectral analysis and numerical methods. Researchers are exploring new approaches to analyze and solve complex systems, including those with nonlinear and non-smooth dynamics. A key direction is the development of innovative numerical schemes, such as the Perturbation Function Iteration Method, which can efficiently handle high-dimensional and non-smooth problems. Another area of focus is the improvement of existing methods, including the computation of Floquet multipliers and subspaces, and the analysis of spectral features in matrix sequences. These advances have the potential to impact various applications, including engineering and physics. Noteworthy papers include: The Perturbation Function Iteration Method, which proposes a novel framework for solving periodic solutions of nonlinear and non-smooth systems. The PhasorArray Toolbox, which provides a user-friendly platform for harmonic analysis and control design. The paper on Validity of relaxation models, which validates relaxation models in numerical schemes for hyperbolic-parabolic systems and proposes a new relaxation model for general multi-dimensional systems.