$L^2$ estimates for the $\bar{\mathrm{\partial }}$ operator

This is a survey article about $L^2$ estimates for the $\bar{\mathrm{\partial }}$ operator. After a review of the basic approach that has come to be called the “Bochner-Kodaira Technique”, the focus is on twisted techniques and their applications to estimates for $\bar{\mathrm{\partial }}$, to $L^2$ extension theorems, and to other problems in complex analysis and geometry, including invariant metric estimates and the $\bar{\mathrm{\partial }}$-Neumann Problem.