This paper explores the generation of large hierarchies of physical scales in string compactifications through the use of RR and NS fluxes. The authors demonstrate that such hierarchies can be naturally realized in string theory, using examples from orientifold compactifications of IIB string theory and F-theory compactifications on Calabi-Yau four-folds. The hierarchy of scales is determined by the choice of fluxes in the compact manifold. The solutions involve compactifications of the Klebanov-Strassler gravity dual to a confining N=1 supersymmetric gauge theory, where the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory. The paper discusses the role of warped compactifications in generating hierarchies, particularly in the context of the Randall-Sundrum (RS) models. It shows that warped metrics are natural in string theory, where D-branes provide sources for the warping. The Verlinde solution, which involves N D3-branes on a Calabi-Yau space, is a simple realization of this. The RS models and Verlinde's warped compactifications allow for large hierarchies but do not explain them. The authors show that additional dynamics can fix the moduli and produce a calculable large hierarchy, as demonstrated by Goldberger and Wise. The paper also discusses the use of fluxes to generate hierarchies, particularly in the context of the Klebanov-Strassler solution. The authors show that the presence of both RR and NS fluxes can lead to a smooth string solution with a large hierarchy. The KS solution is noncompact and thus not suitable for reducing string theory to four dimensions. The authors aim to find true string compactifications with a finite four-dimensional Planck scale and a local region of the KS form that generates a large but finite hierarchy. This hierarchy is determined by the quantized values of the fluxes on the compact manifold. The paper also discusses the global constraints on warped IIB solutions, showing that the presence of negative tension objects such as O3 planes allows for warped compactifications. The authors show that when localized sources satisfy a certain BPS-like bound, the global constraints determine the general solution. The solutions involve compact smooth string solutions with the hierarchy fixed by the fluxes, in a limit of large fluxes. The paper concludes by discussing the implications of these results for the understanding of hierarchies in string theory, showing that the presence of fluxes can lead to a smooth string solution with a large hierarchy. The authors also discuss the relation between these solutions and the dual gauge theory descriptions, showing that the hierarchy is determined by the fluxes and the geometry of the compact manifold. The paper provides a detailed analysis of the constraints and solutions in the context of string theory, showing that the presence of fluxes can lead to a smooth string solution with a large hierarchy.This paper explores the generation of large hierarchies of physical scales in string compactifications through the use of RR and NS fluxes. The authors demonstrate that such hierarchies can be naturally realized in string theory, using examples from orientifold compactifications of IIB string theory and F-theory compactifications on Calabi-Yau four-folds. The hierarchy of scales is determined by the choice of fluxes in the compact manifold. The solutions involve compactifications of the Klebanov-Strassler gravity dual to a confining N=1 supersymmetric gauge theory, where the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory. The paper discusses the role of warped compactifications in generating hierarchies, particularly in the context of the Randall-Sundrum (RS) models. It shows that warped metrics are natural in string theory, where D-branes provide sources for the warping. The Verlinde solution, which involves N D3-branes on a Calabi-Yau space, is a simple realization of this. The RS models and Verlinde's warped compactifications allow for large hierarchies but do not explain them. The authors show that additional dynamics can fix the moduli and produce a calculable large hierarchy, as demonstrated by Goldberger and Wise. The paper also discusses the use of fluxes to generate hierarchies, particularly in the context of the Klebanov-Strassler solution. The authors show that the presence of both RR and NS fluxes can lead to a smooth string solution with a large hierarchy. The KS solution is noncompact and thus not suitable for reducing string theory to four dimensions. The authors aim to find true string compactifications with a finite four-dimensional Planck scale and a local region of the KS form that generates a large but finite hierarchy. This hierarchy is determined by the quantized values of the fluxes on the compact manifold. The paper also discusses the global constraints on warped IIB solutions, showing that the presence of negative tension objects such as O3 planes allows for warped compactifications. The authors show that when localized sources satisfy a certain BPS-like bound, the global constraints determine the general solution. The solutions involve compact smooth string solutions with the hierarchy fixed by the fluxes, in a limit of large fluxes. The paper concludes by discussing the implications of these results for the understanding of hierarchies in string theory, showing that the presence of fluxes can lead to a smooth string solution with a large hierarchy. The authors also discuss the relation between these solutions and the dual gauge theory descriptions, showing that the hierarchy is determined by the fluxes and the geometry of the compact manifold. The paper provides a detailed analysis of the constraints and solutions in the context of string theory, showing that the presence of fluxes can lead to a smooth string solution with a large hierarchy.