The main purpose of Computational Mechanics research is not to obtain more efficient computational methods on existing cases (or more accurate, which is somewhat equivalent). This purpose is to perform new computations which were not affordable before. Future researchers will hopefully be able to face the many challenges of the century (global change, health, energy). This remark holds (to a lesser extend) for mesh adaptation research. The purpose is to be able to compute new phenomena and also to master the numerical uncertainties which have been up to now unsufficiently controlled.Many phenomena in continuum mechanics real world involve multiple scales or/and singularities and cannot computed with uniform meshes. Designing non uniform meshes will become so complex that automatic adaptation will be mandatory.