Presently, Krylov subspace methods are among the common approaches for solving linear systems of equations arising in flow through large-scale porous media. Intensive research is needed to develop suitable preconditioners that can account for extreme properties of the media. Is the information ofrelated systems useful to solve the current system in a faster way?The increasing complexity of various subsurface problems has motivatedthe formulation of more robust preconditioning methods. A more recenttechnique to enhance the convergence further is the reuse of previoussolutions or search direction vectors as deflation vectors. However, a good selection of theavailable vectors is crucial for an efficient method. One way to select and reducethe number of vectors is to combine it with a Proper OrthogonalDecomposition (POD) approach.The objective of this minisymposium is to promote fruitful discussionsto identify commonalities and new avenues of research that may lead tothe development of improved robust and efficient deflationpreconditioners for problems of flow in porous media. Weexpect that this interaction may also shed light on other more general, unexplored issues that exist between Krylov subspace methods and domaindecomposition/multilevel types of solvers.