Brief overview of Candidate de Sitter Vacua

We review compactifications of type IIB string theory which produce de Sitter vacua to leading order in the $α^\prime$ and $g_s$ expansions in line with the scenario proposed by Kachru, Kallosh, Linde, and Trivedi. We detail specific Calabi-Yau orientifold compactifications incorporating the non-perturbative superpotential from Euclidean D3-branes, the full flux-induced superpotential, and the Kähler potential evaluated at string tree level but retaining all orders in $α'$. Each model hosts a Klebanov-Strassler throat featuring a single anti-D3-brane. The energy associated with this supersymmetry-breaking source, computed at leading order in $α'$, lifts the minimum to a metastable de Sitter vacuum with all moduli stabilised. A key open challenge is the identification of vacua that remain stable when including additional corrections; an endeavour for which this study provides a solid foundation. This work is a contribution to the proceedings of the Corfu Summer Institute 2024 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2024) and is based on arXiv:2406.13751.