In 2018, the CNRS Thematic School “M2Corr” (“Mechanics – Microstructure – Corrosion”) brought together some one hundred people around the theme of coupling between mechanics, microstructure and corrosion, under the aegis of CNRS and CEFRACOR. Experts from various academic institutions and stakeholders from a range of industrial sectors discussed and analyzed the state of the art of scientific and technological developments related to the durability of materials and structures subjected to mechanical and environmental stress, coupled or decoupled. The experimental, theoretical and numerical aspects were discussed at different scales. This book, consisting of 22 chapters summarizing the courses taught at this school, provides its readers with the most advanced tools and scientific approaches to: – apprehend the phenomena of coupling by understanding the associated mechanisms, and to identify the variables of the first order among those related to the mechanical state, the material or the chemical environment; and – propose strategies to control and/or extend the life of structures in a multi-process coupling situation. The aim of this chapter is to briefly describe different techniques used for modeling structures from the atomic scale to the macroscopic scale and, where appropriate, their surrounding environment. For each method we will provide the general principle, references to books for more information, strengths and limitations, as well as some examples of recent applications drawn from the literature.