This paper presents the construction of metastable de Sitter (dS) vacua in type IIB string theory. The authors start with highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, they can fix all moduli, yielding a supersymmetric AdS vacuum. Adding a small number of anti-D3 branes allows uplifting the AdS minimum to a metastable dS ground state. The lifetime of these vacua is much longer than the cosmological timescale of 10^10 years. The authors also prove that the lifetime of dS space in string theory is always shorter than the recurrence time. The paper discusses flux compactifications of IIB string theory, including corrections to the no-scale models. They show that incorporating these corrections can yield supersymmetric AdS minima with all moduli stabilized. They then describe how adding anti-D3 branes can uplift the AdS vacuum to a dS vacuum. The resulting dS vacuum has a tunable cosmological constant and is metastable. The authors analyze the stability of the dS vacuum, showing that its lifetime is extremely long compared to the cosmological timescale but much shorter than the recurrence time. The paper also discusses the tunneling probability from a dS vacuum to Minkowski space, showing that the decay time is exponentially smaller than the recurrence time. They consider two approximations for tunneling: the thin-wall approximation and the "no-wall" approximation. The thin-wall approximation is valid when the dS vacuum is very small compared to the height of the barrier, while the "no-wall" approximation is valid when the barrier is very wide. The authors find that the decay time of the dS vacuum is much shorter than the recurrence time, but the vacuum is still extremely stable compared to the cosmological timescale. The paper concludes that the constructions in this paper are reliable and provide a promising arena for the construction of string cosmologies.This paper presents the construction of metastable de Sitter (dS) vacua in type IIB string theory. The authors start with highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, they can fix all moduli, yielding a supersymmetric AdS vacuum. Adding a small number of anti-D3 branes allows uplifting the AdS minimum to a metastable dS ground state. The lifetime of these vacua is much longer than the cosmological timescale of 10^10 years. The authors also prove that the lifetime of dS space in string theory is always shorter than the recurrence time. The paper discusses flux compactifications of IIB string theory, including corrections to the no-scale models. They show that incorporating these corrections can yield supersymmetric AdS minima with all moduli stabilized. They then describe how adding anti-D3 branes can uplift the AdS vacuum to a dS vacuum. The resulting dS vacuum has a tunable cosmological constant and is metastable. The authors analyze the stability of the dS vacuum, showing that its lifetime is extremely long compared to the cosmological timescale but much shorter than the recurrence time. The paper also discusses the tunneling probability from a dS vacuum to Minkowski space, showing that the decay time is exponentially smaller than the recurrence time. They consider two approximations for tunneling: the thin-wall approximation and the "no-wall" approximation. The thin-wall approximation is valid when the dS vacuum is very small compared to the height of the barrier, while the "no-wall" approximation is valid when the barrier is very wide. The authors find that the decay time of the dS vacuum is much shorter than the recurrence time, but the vacuum is still extremely stable compared to the cosmological timescale. The paper concludes that the constructions in this paper are reliable and provide a promising arena for the construction of string cosmologies.