This work summarizes solution strategies for discrete systems occurring in the simulation of processes in the subsurface. The focus is on scalable solvers for large and coupled systems. The goal of this work is to enable researchers to select suitable algorithms and parameter settings to efficiently solve their problems. The work provides an overview of existing methods, highlighting their features, potential, and also frequent pitfalls. Numerical examples are provided for single phase flow, density driven flow and poroelasticity.Aspects of multiphase flow are discussed briefly; a detailed discussion of reactive transport is beyond the scope of the article. Future trends are discussed.