The purpose of this review is to update ( publications from 1981 to mid 2006) the synthetic applications of dealkoxycarbonylations of malonate esters, beta-keto esters (and related esters with alpha-substituted electron-withdrawing functionalities) induced by heating with water or with water in the presence of salts (such as NaCN, NaCl or LiCl) in dipolar aprotic solvents. The presentation will be divided in two parts. In Part 1, discussion will focus on the dealkoxycarbonylations of malonate esters. Part 2 ( to follow as a separate paper) will deal with the dealkoxycarbonylations of beta-keto esters and alpha-cyano esters (and related analogues).