The numerical solution of large problems often requires the usage of (preconditioned) iterative solution methods. Examples are geometric and algebraic multigrid methods, domain decomposition methods, and preconditioned Krylov sub-space methods. Such techniques typically exploit structural properties of the underlying problem and thus have to be carefully modified when applied to Extended Discretization Methods for, e.g., problems with complex geometries, fractures, or internal boundaries. The current lack of robust iterative solvers is one of the main bottlenecks preventing extended discretization approaches being widely used in real-world applications, specially in large-scale simulations with multi-core distributed-memory high-performance computers. In addition, the interest and demand of suitable iterative solvers is rapidly increasing as parallel computers are becoming more and more available. In this MS, we will present and discuss iterative solution methods which are especially designed for extended approaches. We will focus in different aspects such as how iterative solution methods are affected by the structural properties connected to extended discretization methods, or how optimal (parallel) iterative solvers can be derived.