Multiphysics systems are often characterized by the highly nonlinear interaction of a myriad of complex, multiple time- and length-scale physical mechanisms. All of them impact the conditioning of the resulting system of linearized equations to be solved within an iterative nonlinear solver. If solved monolithically, additional challenges arise from the block structure of the system matrix. For the robust, efficient, and scalable solution of the most challenging systems in science and engineering applications, custom-built iterative methods and/or physics-informed approximate block factorization preconditioners are required. This minisymposium addresses the most important and active research topics for iterative methods and block preconditioning for challenging multiphysics systems, including - preconditioned iterative solvers for multiphysics systems - physics-based block preconditioning - multi-level and multi-domain preconditioners - approximate block factorizations - the interplay of physics, algorithms, implementation, and hardware aspects for applications in solid mechanics, e.g. contact and fracture problems, surface-coupled problems such as fluid-structure interaction, and volume-coupled problems, e.g. reactive flows, magneto-hydrodynamics, or plasma physics applications, among others. Concerned with coupled systems of equations arising from multiphysics and multiscale discretizations, this minisymposium aims to provide a forum for researchers to discuss promising developments and advances in iterative methods in general and block preconditioning for large sparse linear systems of equations in particular.