The field of numerical analysis is witnessing significant developments in eigenvalue computations and spectral analysis. Research is focused on improving the efficiency and accuracy of algorithms for computing eigenvalues and eigenvectors, particularly for large-scale problems. Innovative approaches, such as the use of eigenvalue perturbation theory and bi-orthogonal structure-preserving methods, are being explored to address the challenges of computing pseudospectral abscissas and solving linear response eigenvalue problems. Furthermore, spectral element methods and complex scaling techniques are being applied to simulate wave propagation and scattering phenomena in various fields, including physics and engineering. Notable papers include: the proposal of a fixed-point iteration method based on eigenvalue perturbation theory for approximating the pseudospectral abscissa, the development of a bi-orthogonal structure-preserving eigensolver for large-scale linear response eigenvalue problems, and the introduction of a new semi-discrete modulus of smoothness for one- and two-sided error estimates in approximation theory.