%0 Journal Article %T $L^2$ estimates for the $\bar \partial$ operator %A Jeffery D. McNeal %A Dror Varolin %J Mathematics %D 2015 %I arXiv %X 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. %U http://arxiv.org/abs/1502.08047v1