We give an overview of moduli stabilization in compactifications of string
theory. We summarize current methods for construction and analysis of vacua
with stabilized moduli, and we describe applications to cosmology and particle
physics. This is a contribution to the Handbook of Quantum Gravity.Comment: 74 pages. Invited chapter for the Handbook of Quantum Gravity (edited
  by Cosimo Bambi, Leonardo Modesto, and Ilya Shapiro, Springer 2023