The field of numerical methods for wave equations and elasticity problems is experiencing significant developments, with a focus on improving the accuracy and efficiency of existing methods. Researchers are exploring new approaches to domain decomposition, finite element analysis, and boundary element methods to tackle complex problems in acoustic scattering, elastic waves, and fluid-structure interaction. Notably, innovative techniques such as non-iterative domain decomposition time integrators and space-time adaptive boundary element methods are being proposed to enhance the performance of numerical simulations. Additionally, there is a growing interest in developing efficient preconditioning techniques for iterative solvers to address the challenges posed by large, indefinite linear systems. Some noteworthy papers in this area include: A non-iterative domain decomposition time integrator combined with discontinuous Galerkin space discretizations for acoustic wave equations, which enables higher-order approximations and heterogeneous material parameters. Preconditioning of GMRES for Helmholtz problems with quasimodes, which derives a convergence bound and illustrates the impact of deflation techniques on GMRES performance.