The numerical solution of systems of PDEs, which describe the behavior of multi-physical phenomena and processes, typically requires the application of efficient linear and non-linear solvers. This is particularly relevant for problems that include a large number of fields, e.g., phase field modeling of grain growth and solidification of or reaction-diffusion in multi-component alloys. These problems require a high spatial resolution increasing the number of unknowns. Therefore, the application of direct (linear) solvers becomes too computationally expensive, and an iterative method has to be employed. However, a suitable preconditioner is essential for iterative solvers to converge within a reasonable number of iterations. Domain decomposition based preconditioners or multi-grid methods are suitable methods of choice, however, their performance, scalability and efficiency crucially depends, among other things, on the construction of the preconditioner. Furthermore, load balancing and updates of the domain decomposition are essential for scenarios, in which adaptive spatial discretization techniques are employed, while reutilization of preconditioners or nonlinear preconditioning techniques are of interest in coupled, nonlinear problems. This minisymposium aims to explore the latest developments in iterative solvers and their associated preconditioners applied to multi-physics problems using monolithic and staggered approaches. Discussions will highlight large-scale simulations on state of the art high performance compute clusters using established software libraries like Trilinos, PETSc and deal.II.