The paper discusses the generation of large hierarchies of physical scales in string theory through warped compactifications. The authors demonstrate that this mechanism is realizable in string theory, particularly in orientifold compactifications of IIB string theory and F-theory compactifications on Calabi-Yau four-folds. The hierarchy is determined by the choice of RR and NS fluxes in the compact manifold. The solutions involve compactifications of the Klebanov-Strassler gravity dual to a confining $\mathcal{N} = 1$ supersymmetric gauge theory, where the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory. The introduction highlights the puzzle of the small ratio $M_{\text{weak}}/M_{\text{Planck}}$ and explores various mechanisms for producing such a hierarchy, including dimensional transmutation, nonperturbative effects, and warped spacetime. The authors focus on the latter, noting that warped metrics are natural in string theory due to D-branes providing sources for warping. They discuss the limitations of previous models, such as the Randall-Sundrum (RS) models, and propose a new approach using fluxes to fix the moduli and produce a calculable hierarchy. The paper outlines the global constraints on warped IIB solutions and the local structure of compactifications, emphasizing the role of localized sources like D3-branes, wrapped D7-branes, and O3-planes. It derives the necessary conditions for a solution and discusses the supersymmetry properties. The authors also explore the effective four-dimensional actions and moduli stabilization. Finally, the paper provides explicit examples of warped compactifications, including orientifolds of CY compactifications and F-theory compactifications, to illustrate the construction of consistent solutions with both negative D3 charge/tension and flux configurations.The paper discusses the generation of large hierarchies of physical scales in string theory through warped compactifications. The authors demonstrate that this mechanism is realizable in string theory, particularly in orientifold compactifications of IIB string theory and F-theory compactifications on Calabi-Yau four-folds. The hierarchy is determined by the choice of RR and NS fluxes in the compact manifold. The solutions involve compactifications of the Klebanov-Strassler gravity dual to a confining $\mathcal{N} = 1$ supersymmetric gauge theory, where the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory. The introduction highlights the puzzle of the small ratio $M_{\text{weak}}/M_{\text{Planck}}$ and explores various mechanisms for producing such a hierarchy, including dimensional transmutation, nonperturbative effects, and warped spacetime. The authors focus on the latter, noting that warped metrics are natural in string theory due to D-branes providing sources for warping. They discuss the limitations of previous models, such as the Randall-Sundrum (RS) models, and propose a new approach using fluxes to fix the moduli and produce a calculable hierarchy. The paper outlines the global constraints on warped IIB solutions and the local structure of compactifications, emphasizing the role of localized sources like D3-branes, wrapped D7-branes, and O3-planes. It derives the necessary conditions for a solution and discusses the supersymmetry properties. The authors also explore the effective four-dimensional actions and moduli stabilization. Finally, the paper provides explicit examples of warped compactifications, including orientifolds of CY compactifications and F-theory compactifications, to illustrate the construction of consistent solutions with both negative D3 charge/tension and flux configurations.