This minisymposium invites contributions on cutting-edge developments in the numerical approximation of time-dependent partial differential equations. The focus is on innovative high-order space-time discretization techniques, including finite element methods and isogeometric analysis, as well as domain decomposition and parallelization strategies, and advanced iterative solvers and preconditioners. The minisymposium aims to foster exchange between theoretical advances and real-world applications, bringing together researchers interested in pushing the boundaries of large-scale computational science.