  This is a survey article about $L^2$ estimates for the $\bar \partial$
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 $\bar \partial$, to $L^2$ extension theorems, and
to other problems in complex analysis and geometry, including invariant metric
estimates and the $\bar \partial$-Neumann Problem.
