This paper is devoted to a thorough study on convex analysis approach to dc (difference of convex functions) programming and gives the State of the Art. Main results about dc duality, local and global optimalities in dc programming are presented. These materials constitute the basis of the DCA (dc algorithms). Its convergence properties have been tackled in detail, especially in dc polyhedral programming where it has finite convergence. Exact penalty, Lagrangian duality without gap, and regularization techniques have beeen studied to find appropriate dc decompositions and to improve consequently the DCA. Finally we present the application of the DCA to solving a lot of important real-life dc programs.