Large scale Mixed Integer Programming (MIP) optimization models are intricate to solve. When the model decomposes into blocs, for instance when optimizing the use of multiple ressources, relaxing the linking constraints in a Lagrangian way can make the model tractable. Exploiting such decomposition to develop tight approximations has lead to tremendous progress in solving important applications. In this presentation, we review the alternative methods to solve the so-called Lagrangian dual model or its linear programming counterpart, the Dantzig-Wolfe master (associated with the column generation algorithm). We highlight their drawbacks, their common base, and their specific features, while discussing extentions of such methods.