Time integration plays a fundamental role in the numerical simulation of complex multiscale and multiphysics systems, where disparate temporal scales and tightly coupled physical processes challenge existing algorithms. This minisymposium brings together researchers to discuss the design, analysis, and application of modern time discretization techniques. Presentations will span theoretical analysis, algorithmic development, and practical implementations, exploring topics that include high-order Runge-Kutta methods, geometric and structure-preserving integrators, adaptive and multirate time-stepping, exponential and IMEX methods, and time integration for coupled multiscale and multiphysics problems. By highlighting both methodological innovations and application-driven developments, the session seeks to promote interdisciplinary collaboration and advance the state of the art in time integration.