In this chapter, I review how overpressure is generated and preserved in sedimentary basins. I begin by describing how pore pressure is generated and how it dissipates under conditions of uniaxial strain. I then explore the overpressure that results during sedimentation under conditions of vertical uniaxial strain. I present several numerical solutions in one and two dimensions to extend these concepts. I illustrate how these types of basin models provide insight into the evolution of pressure and stress in basins. I also use these results to explore the role of thermal expansion and smectite-illite diagenesis in generating pore pressure. I then discuss hydromechanical models that couple the full stress state with pore fluid flow under three-dimensional strain. I use these models to illustrate the role of non-uniaxial loading in salt systems and thrust belts. Finally, I explore the potential role of viscous compaction in pore pressure generation.